Mathematical Sciences is a double-blind peer-reviewed open access journal published. The journal publishes original research articles that demonstrate the interaction between various disciplines of theoretical and applied mathematics. Subject areas include numerical analysis, numerical statistics, optimization, operational research, signal analysis, wavelets, image processing, fuzzy sets, spline, stochastic analysis, integral equation, differential equation, partial differential equation and combinations of the above. This journal operates on an open access model and charges an Article Processing Charge (APC) to cover the costs of publication and ensure free and permanent access to published articles. We are committed to supporting researchers worldwide and offer APC waivers for authors from low- and middle-income countries, as well as in cases of financial hardship. Waiver requests are considered on a case-by-case basis and do not influence editorial decisions. For more information on APCs and waiver eligibility, please visit our APC & Waivers Policy page. Journal DOI: 10.57647/ms Journal Abbreviation: Math. Sci. Journal Title Acronym: MS Journal Owner: Islamic Azad University Publisher: Islamic Azad University, Co-publishing, OICC Press, UK Editor-in-Chief: Khosro Maleknejad, PhD Director-in-Charge & Managing Editor: Morteza Khodabin, PhD Submit Manuscript: https://mc04.manuscriptcentral.com/mathsc
Proportional Hazard Bivariate Chen Model and Its Mathematical Features with Applications on Environmental, Climatic and Medical Data
This paper introduces a new bivariate model, the Bivariate Chen Proportional Hazard Rate (BCPH) model, designed to effectively model diverse real-life datasets. This model is formulated within the proportional hazard framework, employing Chen marginal distributions. Its main statistical and reliability characteristics such as product moments, Pearson’s correlation, survival, and hazard functions are thoroughly derived and analyzed. Parameter estimation is accomplished through the maximum likelihood method and inference functions for margins, with simulation studies confirming the consistency and efficiency of the estimators. The BCPH model is further applied to various environmental, climatic, and medical datasets, including mercury fish length, precipitation temperature, and kidney infection recurrence times. Comparative evaluations using AIC, BIC, CAIC, and HQIC criteria demonstrate that the BCPH distribution provides a superior fit compared to existing bivariate models, highlighting its robustness, flexibility, and suitability for real world applications.
Copyright (c) 2026 N. M. Kilany, Asamh Saleh M. Al Luhayb, Reid Alotaibi, Lobna H. El-Refai (Author) https://creativecommons.org/licenses/by/4.0
A Survey: Kannan Fixed Point Theorem in Hyperconvex Spaces
We prove that every closed ball in a non-reflexive Banach space ℓ∞ is a proximinal set. We also define a concept of ℏ-proximal quasi-normal structure on a pair of nonempty and admissible subsets of a metric space and prove that every nonempty and admissible pair of subsets of a hyperconvex metric space has the ℏ-proximal quasi-normal structure. We then discuss best proximity theory by considering two family of cyclic maps entitled cyclic Kannan contractions and cyclic relatively Kannan nonexpansive mappings and show that every cyclic Kannan contraction defined on a union of two nonempty and admissible subsets of a hyperconvex metric space has a best proximity point and by using the geometric notion of ℏ-proximal quasi-normal structure, we conclude a similar result for cyclic relatively Kannan nonexpansive maps which preserves distance. In a special case, we obtain Baillon’s fixed point theorem for Kannan nonexpansive self-mapping.
Copyright (c) 2026 Moosa Gabeleh, Jack Markin (Author) https://creativecommons.org/licenses/by/4.0
Hybrid Fuzzy Regression: Performance Comparison of Symmetric and Asymmetric Triangular Fuzzy Data
This paper presents a comprehensive comparison between symmetrical and asymmetrical triangular fuzzy data within hybrid bivariate regression models, evaluating their performance through reliability measures and uncertainty quantification. Our study demonstrates that hybrid least squares fuzzy regression not only gener-alizes classical regression but also provides superior reliability metrics, with classical measures emerging as a special case of hybrid measures emerging as a special case of hybrid reliability under precise conditions.
Copyright (c) 2026 Reza Hozni, Behrouz Fathi Vajargah, Mohamad Hassan Behzadi, Mojtaba Moradi (Author) https://creativecommons.org/licenses/by/4.0
Reliability Analysis of Log-Exponential Transformations under Progressive type-II Censoring with Medical Applications
In the present paper, we propose a flexible and comprehensive family of distributions derived using the Log-Exponential transformation method within the framework of the progressive type-II censoring scheme. This new family is adaptable to various data types, as its probability density function can assume multiple forms. Beyond presenting this flexible family, we study its statistical properties and invariant estimation techniques, including the maximum likelihood and maximum product spacing estimation. We also conduct a reliabil-ity analysis of the new family, with a focus on the modified Weibull distribution as a special case. The Monte Carlo simulations are provided to assess the performance of the proposed estimation methods of the parameters and reliability function under the progressive type-II censoring. Our study emphasizes mod-eling COVID-19 data using this new family and performing reliability analysis under progressive type-II censoring, accompanied by a thorough discussion on estimation. The applicability of the proposed family is demonstrated using two COVID-19 data sets and comparisons with competitor distributions.
Copyright (c) 2026 Peyman x Peyman Senobari, Mohsen Kokabinezhad, Ezzatallah Baloui Jamkhaneh, Leila Golshani (Author) https://creativecommons.org/licenses/by/4.0
Approximate Null Controllability of Atangana–Baleanu Fractional Stochastic Evolution Equations with Poisson Jumps and Fractional Brownian Motion
This paper investigates the approximate null controllability of a class of Atangana–Baleanu fractional stochas-tic evolution equations in a separable Hilbert space, driven simultaneously by a fractional Brownian motion and a Poisson random measure. The system is governed by the Caputo-type Atangana–Baleanu fractional derivative of order ???? ∈ (1/2, 1), a linear operator generating an ????-resolvent family, a bounded linear con-trol operator, and nonlinear terms satisfying suitable growth and integrability conditions. Assuming that the associated linear system is approximately null controllable and imposing standard Carathéodory-type assump-tions on the nonlinearities, we derive sufficient conditions ensuring the approximate null controllability of the full nonlinear stochastic system in the mean-square sense. The analysis relies on the variation-of-constants formula associated with fractional resolvent families, mean-square estimates for stochastic integrals with re-spect to fractional Brownian motion and compensated Poisson random measures, and a Schauder fixed point argument in an appropriate space of stochastic processes. An illustrative example involving a controlled Atangana–Baleanu fractional stochastic partial differential equation with Dirichlet boundary conditions is provided to demonstrate the applicability of the abstract results.
Copyright (c) 2026 Yazid Alhojilan (Author) https://creativecommons.org/licenses/by/4.0
Heat Transfer Investigation of Dissipative Couple Stress Rotating Fluid: Numerical and Theoretical Treatments
A comprehensive numerical study is presented to investigate heat transfer in the boundary layer flow of an incompressible fluid with a couple stress resulting from a permeable plate and linear extension. The model accounts for the combined influence of a transverse magnetic field and system rotation, where the inclusion of the Coriolis force introduces an additional rotational resistance that alters the flow structure. Fluid properties and wall permeability are systematically examined to assess their roles in shaping the thermal behavior. The thermal analysis is performed under a prescribed surface temperature condition, allowing for a clear eval-uation of heat transport mechanisms. Moreover, the formulation incorporates both viscous dissipation and energy due to couple stresses, which are essential in accurately capturing the physics of such fluids. These considerations are particularly relevant in processes associated with the manufacturing and handling of mag-netic materials, where rotational and electromagnetic effects coexist and significantly impact heat transfer characteristics. Similarity transformations create a nonlinear set of coupled ODEs with boundary conditions from the governing equations. The merged Fibonacci-Lucas polynomials (MFLPs) are used as part of the problem-solving strategy, along with the least-squares approximation technique, to simplify the equations that define the mathematical model into a nonlinear system of algebraic equations, then solved by Newton iteration approach. The research also includes examining the convergence and estimating the error of the proposed scheme. The results reveal that increasing the couple stress factor can slightly enhance skin fric-tion (3.5%) but significantly reduces heat transfer (26.7%), while increasing the magnetic field parameter markedly decreases both skin friction (50.4%) and heat transfer (23.9%). The discussion revolves around how relevant parameters affect the fluid’s temperature and velocity profiles. The technique’s effectiveness is shown through a table comparison, indicating good alignment with existing data and highlighting its accuracy.
Copyright (c) 2026 Mohamed M. Khader, Mohamed Adel, Amel A. Alaidrous (Author) https://creativecommons.org/licenses/by/4.0
A Robust Galerkin Fractional Taylor Technique to Solve Multi-Dimensional Fractional Optimal Control Problems with Inequality Constraints
A new computational approach is presented for solving MFOCPs subject to Caputo fractional dynamics by means of Galerkin projection technique along with fractional Taylor polynomial expansions. The method successfully deals with constraints in the form of both equalities and inequalities. An important feature of the new method includes deriving an operational matrix based on fractional Taylor polynomials such that, using the Galerkin approach, the problem under study is reduced to a set of algebraic equations. Convergence analysis of the Taylor series expansions is investigated in detail. The performance of the approach is confirmed by applying it to four problems in comparison with other existing approaches in the literature. MSC 2010: 49M05; 65T60
Riemann-Liouville fractional integral (RLI)
Copyright (c) 2026 Lakhlifa Sadek, Ibtisam Aldawish, Zakia Hammouch, Ahmad Shafee, Ioan-Lucian Popa (Author) https://creativecommons.org/licenses/by/4.0
Solving Multi-order Nonlinear Caputo Fractional Differential Equations and Numerical Simulations
This paper addresses the challenging problem of establishing the existence and uniqueness of solutions for coupled multi-order fractional differential equations involving multiple fractional orders, a class of equations that arises in various scientific and engineering applications. By employing the powerful Banach contraction principle, we derive novel sufficient conditions that guarantee the existence and uniqueness of solutions. The theoretical findings are further substantiated through the presentation and analysis of a detailed illustrative example, highlighting the practical relevance of our results. To validate the theoretical results, we implement a modified Adams-Bashforth-Moulton predictor-corrector method for the numerical solution of the proposed multi-term Caputo fractional differential systems. In particular, three illustrative examples are presented to demonstrate the impact of fractional orders and memory effects on system dynamics. These simulations, covering nonlinear coupled oscillators, neural feedback processes, and epidemic models. The results confirm the robustness of the theoretical framework and the applicability of the method to real-world problems governed by fractional dynamics.
Copyright (c) 2026 Manal Elzain Mohamed Abdalla, Hasanen A. Hammad, Tarek Aboelenen (Author) https://creativecommons.org/licenses/by/4.0
High-Order Taylor Collocation Methods for Linear Matrix Differential Equations: Theory and Computation
The paper develops a numerical technique employing Taylor polynomial expansion and collocation to solve linear matrix differential equations of first order. The proposed technique converts the original differential matrix equation into a set of algebraic equations using matrix manipulations such as Kronecker products and vectorization of matrices. An error analysis is performed to show the sound theoretical background of the developed technique. Numerical investigations prove that the proposed Taylor collocation technique is more efficient than the Bernstein polynomial technique. Moreover, the accuracy and performance of the presented technique have been shown analytically as well as numerically.
Copyright (c) 2026 Junjie Li (Author) https://creativecommons.org/licenses/by/4.0
Efficient Numerical Solutions of Proportional Fractional Differential Equations
This article proposes a new family of basis functions named exp-Bernstein functions, which generalize classical Bernstein polynomials by adding an exponential term that is compatible with proportional fractional derivatives. These functions are tailored to efficiently treat generalized proportional fractional calculus operators. We propose a numerical method using exp-Bernstein functions and a collocation method for solving linear and nonlinear generalized proportional fractional Cauchy problems (GPFCPs). Our method uses an operational matrix approach to calculate proportional fractional derivatives exactly. Theoretical convergence results are also given, providing error estimates using fractional Gronwall inequalities. Numerical results show that the proposed method provides high accuracy. The exp-Bernstein basis function is particularly useful for problems with exponential kernels, which are typical of proportional fractional derivatives.
Proportional fractional derivatives (PFD)
Copyright (c) 2026 Lakhlifa Sadek, Ali Algefary (Author) https://creativecommons.org/licenses/by/4.0
Solvability and Stability for a Tripled System of Fractional Integro-differential Equations under Integral Boundary Conditions
This article investigates the solvability and stability of a nonlinear tripled system of fractional integro-differential equations via integral boundary conditions. We prove the fundamental existence and uniqueness results for the solution using powerful methods from nonlinear functional analysis, including the Banach fixed-point theorem. Crucially, we gauge the system’s resistance to small perturbations using Ulam-Hyers stability analysis. Our results confirm that approximate solutions are close to the true solution, providing an essential resilience measure for complex models in which memory and hereditary traits are captured by fractional derivatives. Finally, an illustrative example has been presented to validate the stated theoretical results.
Copyright (c) 2026 Hasanen A. Hammad, Doha A. Kattan (Author) https://creativecommons.org/licenses/by/4.0
On the Existence and Stability of Solutions for Implicit Coupled Neutral Fractional Differential Systems
This paper investigated the existence, uniqueness, and stability behavior of a class of non-linear implicit coupled neutral fractional differential equations governed by the Caputo-Atangana-Baleanu derivative. The existence of solutions was obtained by applying Krasnoselskii’s fixed-point theorem, whereas the Banach contraction principle was employed to establish both existence and uniqueness results. Furthermore, several important stability concepts were analyzed, namely Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability, and generalized Ulam-Hyers-Rassias stability. To illustrate the applicability of the developed theory, suitable examples were presented, validating the solvability and stability results for the proposed system. MSC (2020): 35A23, 47H10, 47H09, 26A33
Neutral fractional differential equation
Copyright (c) 2026 Hasanen A. Hammad, Sami Baraket, Hassen Aydi (Author) https://creativecommons.org/licenses/by/4.0
Survival Analysis Based on the AFT Approach with a Semi-Continuous Response under Zero-Inflation:An Application in Life Insurance
Mortality models in actuarial science are important tools used to develop models from historical data to predict future trends and mortality rates, particularly in life insurance and premium assessments. These models need to be flexible enough to accommodate effects such as age and product type. Censoring also features as a unique element providing a basis for survival analysis, as it is not very often that the entire duration values are present as non-negative or asymmetric for various censored cases. Standard regression methods are unsuitable for such data, and specialized techniques such as Cox Proportional Hazards and Accelerated Failure Time (AFT) models are required. AFT models allow for flexible distributional assumptions while providing interpretable results in complex settings. This study extends the AFT framework by introducing a Zero-Inflation compo-nent to accommodate semi-continuous lifetime data characterized by excess zeros, thereby transforming a purely continuous distribution into a semi-continuous one. By integrating zero inflation with both right- and left-censoring mechanisms, the proposed models expand the applicability of survival analysis in actuarial contexts. The empirical analysis is based on a real dataset obtained from a medium-sized pension fund, including individual-level information on future lifetimes and relevant covariates. The results demonstrate that the zero-inflated Gompertz AFT model provides superior performance compared to competing specifications, particularly in capturing tail behavior and age-dependent mortality dynamics. Furthermore, the inclusion of zero inflation significantly improves model flexi-bility and estimation accuracy in the presence of excess-zero observations. From an actuarial perspective, the proposed modelling framework offers improved estimation of survival patterns and annuity factors, supporting more accurate longevity risk assessment and better-informed decision-making in life insurance and pension applications.
Copyright (c) 2026 Nafiseh Khojasteh Bakht, Shirin Shoaee, Ehsan Bahrami Samani (Author) https://creativecommons.org/licenses/by/4.0
An Efficient Numerical Approach for Solving the Mittag-Leffler Fractional Differential Equations
In this paper, we introduce a fractional integral operator related to the recently proposed Mittag-Leffler-Caputo-Fabrizio (MLCF) fractional derivative, which has a non-singular Mittag-Leffler kernel. We provide sufficient conditions for the existence of unique solutions for a certain class of nonlinear fractional differential equations by fixed point methods. Our analysis yields an explicit inequality involving fractional orders, the Lipschitz constant, and the finite time, thus guaranteeing the existence of a unique solution. Furthermore, we introduce a novel numerical scheme, the Euler MLCF method, for approximating the solutions to these equations. We prove that this scheme is convergent with first-order accuracy. The new scheme is rigorously validated through numerous numerical examples. The results, in terms of absolute error and empirical convergence order, are consistent with the theoretical prediction. This paper presents theoretical and practical advancements in solving fractional differential equations using the MLCF operator.
Copyright (c) 2026 Lakhlifa Sadek, Ibtisam Aldawish (Author) https://creativecommons.org/licenses/by/4.0
Power Unit Haq Distribution: A Flexible Probability Model for Lifetime Data Analysis
In this study, a new unit interval distribution defined on the unit interval is developed through a power transformation approach and termed the Power Unit Haq (PUH) distribution. Several key statistical properties of the new distribution are derived, including incomplete moments, moments, and associated measures, moment generating function, hazard function, mean residual life function, and Rényi entropy. The parameters of the proposed distribution are estimated using five estimation approaches, and their performance is evaluated through extensive Monte Carlo simulations. The flexibility and practical relevance of the new distribution are further demonstrated by utilizing three real datasets-one involving radiation, reactor pump failures, and kidney dialysis patients. The proposed distribution exhibits superior fitting performance compared to established competing unit interval distributions. Additionally, Bayesian estimation of the model parameter is carried out, enhancing the distribution’s applicability for real-world scenarios.
Copyright (c) 2026 Mohammed Ahmed Alomair, Muhammad Ahsan-ul-Haq (Author) https://creativecommons.org/licenses/by/4.0
Existence, Uniqueness, and Stability Analysis of Coupled Fractional Differential Equations with Hilfer and Weighted Caputo Derivatives
In this paper, we first establish the necessary conditions for the existence, uniqueness, and stability of solutions to system (1) by applying an alternative fixed-point theorem. We then provide specific examples and utilize the Banach fixed-point numerical method to demonstrate the applicability and reliability of our approach; notably, one of these examples is solved numerically in full, and the results from this numerical approximation further confirm the effectiveness and accuracy of the proposed method. These results verify the feasibility of the proposed approach for approximating solutions to complex fractional differential systems.
Copyright (c) 2026 Safoura Tavousi, Reza Saadati, Mohammad B. Ghaemi, Hengameh Tamimi (Author) https://creativecommons.org/licenses/by/4.0
On the Lie Symmetry Analysis of the Time-Fractional Gross-Pitaevskii Equation: A Comparative Study of Riemann-Liouville and Caputo Derivatives
This study develops a detailed Lie symmetry analysis for the one-dimensional time-fractional Gross–Pitaevskii equation (TFGPE), emphasizing how the adopted fractional derivative-Riemann-Liouville (RL) versus Caputo-modifies the symmetry algebra, nonlocal conservation laws, and invariant solution families. The complex-valued model is rewritten as an equivalent coupled system of real partial differential equations, and the corresponding infinitesimal generators are derived in a unified and systematic manner for both fractional formulations. We show that, in the Caputo setting, the standard global ????(1) phase invariance is retained, whereas in the RL formulation this key symmetry is destroyed because the associated initial data are not invariant and the fractional operator does not transform covariantly. Leveraging the resulting symmetry groups, we obtain similarity reductions and construct group-invariant solutions, and we further establish nonlocal conservation laws by applying Ibragimov’s nonlinear self-adjointness approach. Overall, our findings indicate that the selection of the fractional derivative is not a purely technical choice; it decisively affects physical consistency, the admissible symmetry structure, and the conservation behavior of fractional quantum models. The analysis offers a direct RL-Caputo comparison and supports the Caputo derivative as the more suitable framework for preserving the inherent symmetries of quantum systems.
Time-fractional Gross-Pitaevskii equation
Copyright (c) 2026 Parastoo Kabi-Nejad Kabi-Nejad (Author) https://creativecommons.org/licenses/by/4.0
A Robust Numerical Scheme for Three-Dimensional Time-Space Fractional PDEs Using Cubic Spline and Meshless Methods
This paper investigates the numerical solution of a three-dimensional time–space fractional functional partial differential equation involving Caputo fractional derivatives in time and Riesz fractional derivatives in space. Owing to the inherent difficulties associated with fractional operators, such as weakly singular kernels and strong nonlocality, conventional numerical methods often encounter limitations in terms of accuracy and computational efficiency. To address these challenges, a hybrid numerical scheme is developed in which the Caputo fractional derivative is discretized by means of cubic spline interpolation, providing high-order tem-poral accuracy, while advanced meshless techniques are employed for the spatial approximation of the Riesz fractional derivative, thereby effectively managing its global support and singular behavior. The resulting fully discrete scheme is rigorously analyzed, and its unconditional stability is established using the energy method. Extensive numerical experiments on various three-dimensional domains demonstrate the high ac-curacy of the proposed method, with convergence rates consistent with the theoretical analysis, as well as favorable computational efficiency. Overall, the proposed approach offers a robust and flexible computa-tional framework for the numerical treatment of complex fractional models arising in physics, engineering, and applied sciences.
Copyright (c) 2026 Mousa J. Huntul (Author) https://creativecommons.org/licenses/by/4.0
A Novel Extension of the Marshall-Olkin Distribution: Reliability, Mathematical Properties, and Applications in Different Sciences
This paper introduces a new and flexible family of continuous probability distributions, referred to as the Exponentiated Chen Marshall–Olkin family. The linear representation of the proposed model is derived, and several of its statistical properties, including moments, quantile function, Rényi entropy, and reliability measures, are investigated. Parameter estimation for this family is discussed using the maximum likelihood method under both complete and right-censored samples, while three distance-based estimation approaches are also considered. A particular sub-model of this family, called the Exponentiated Chen Marshall-Olkin Weibull distribution, is also proposed and studied in detail. Its mathematical characteristics and related sub-models are explored, and four different estimation techniques-maximum likelihood, least squares, weighted least squares, and Anderson-Darling-are employed to estimate the unknown parameters. Furthermore, a comprehensive simulation study is conducted to assess the bias and mean square error of the estimators, followed by applications to real health and engineering datasets. The empirical results demonstrate that the Exponentiated Chen Marshall–Olkin family provides excellent flexibility for modeling data exhibiting skewness, heavy tails, reliability characteristics, and non-monotonic hazard rates, confirming its potential as a powerful tool in reliability and lifetime data analysis.
Copyright (c) 2026 Elham Moradi, Zahra Shokooh Ghazani (Author) https://creativecommons.org/licenses/by/4.0
A New Method for Nonlinear Katugampola Fractional Differential Equations
In this article, we propose a new wavelet method for solving nonlinear Katugampola fractional differential equations on an arbitrary interval. We have introduced a new wavelet, which we named as the Katugam-pola Gegenbauer wavelet (KGW), and constructed its new operational matrices of Katugampola fractional integrations as well as Katugampola fractional derivatives. The Katugampola Gegenbauer wavelet and its operational matrices are combined with the Adomian polynomials to propose a new method for the solution of nonlinear Katugampola fractional differential equations. The purpose of using the Adomian polynomials is to handle the nonlinearities in the equations. Furthermore, we have provided a detailed methodology for implementing the proposed approach to nonlinear Katugampola fractional differential equations. A detailed error analysis is also performed for the proposed method. The proposed method is implemented on several nonlinear Katugampola fractional differential equations to show the reliability, efficiency, and accuracy of the method.
Katugampola fractional differential equations
Copyright (c) 2026 Maham Bint-e-Ali, Shafaq Idrees, Umer Saeed (Author) https://creativecommons.org/licenses/by/4.0
Effect of Rotation on Wave Propagation in Micro-elongated Thermo-elastic Media with Fractional Conformable Derivative under the Refined Dual-Phase-Lag Model
This study investigates the impact of rotation on wave propagation within a micro-elongated thermoelastic medium, employing the fractional conformable derivative under Lord-Shulman (L-S) theory, the Dual-Phase-Lag (DPL) model, and the Refined Dual-Phase-Lag (RDPL) model. The governing equations for heat conduction, mechanical motion, and micro-elongation are formulated to account for finite thermal wave speeds and microstructural effects. By applying non-dimensionalization and normal mode analysis, the coupled system is transformed into analytically solvable form. Explicit solutions for displacement, temperature, stress, and micro-elongation fields are obtained. Numerical results compare L-S, DPL, and RDPL models with and without rotation, and assess the effect of fractional order. The results show that rotation significantly influences wave propagation characteristics such as amplitude, speed, and attenuation.
Copyright (c) 2026 Ahmed Ramady, Mohamed F. Ismail, Hamdy M. Ahmed, Soliman Alkhatib, Elsaid M. Ramadan, Eslam Nabil Shawki El-Ganzoury (Author) https://creativecommons.org/licenses/by/4.0
An Improved Extension of Unit Moment Exponential Distribution: Mathematics, Inference, and Applications
This study contributes to the derivation of a bounded probability model for unit interval data analysis. The proposed model is named the Sine Unit Moment Exponential (SUME) distribution. This SUME model has the potential to model both the monotone increase and the bathtub shape for the hazard function. We investigate various statistical properties, including mixture representation, moments, quantile function, mean residual life function, and order statistics. The parameter estimation of the SUME distribution is discussed using six different estimation approaches. A comprehensive simulation study is performed to assess frequentist properties of the considered estimation methodologies. Two different datasets related to failure time and milk production are utilized to evaluate the practicality and flexibility of the proposed distribution over renowned unit interval distributions.
Copyright (c) 2026 Bayan Adel Shukr (Author) https://creativecommons.org/licenses/by/4.0
Rotation Effects on a Nonlocal Micropolar Double-Porous Medium with Variable Conductivity and Initial Stress Using MGT Theory
This study investigates the two-dimensional behavior of a nonlocal micropolar double-porous thermoelastic material with voids (MDPTMWV) within the framework of the Moore–Gibson–Thompson (MGT) theory. An isotropic, homogeneous, initially stressed, rotating thermoelastic half-space with double porosity is considered. The MGT heat conduction model, incorporating memory-dependent derivatives and variable thermal conductivity, is employed. Governing equations are derived using generalized thermoelasticity, and analytical solutions for displacement, temperature, equilibrated stress, and thermal stress components are obtained via Lame’s potentials combined with normal mode analysis. The model is analyzed under boundary conditions including variable temperature, normal stress, constant equilibrated stress, and stress-free surfaces. Numerical evaluations using MATHEMATICA illustrate the effects of time, rotation, initial stress, and nonlocal parameters. The results indicate that double porosity and the considered parameters significantly amplify material responses, particularly under increasing time, rotation, initial stress, and nonlocal effects. Several special cases are discussed and validated against the literature. These findings provide insights relevant to geophysics, seismology, and earthquake engineering.
Copyright (c) 2025 Doaa. M. Salah, A.M. Abd-Alla, SMM El-Kabeir, Kawther K. Alarfaj (Author) https://creativecommons.org/licenses/by/4.0
Photo-electro-magneto-thermoelastic Excitation Rotating Semiconductor Medium based on Focused Laser Beam
This study aims to develop an advanced model for the propagation of photo electro-magneto-thermoelastic waves in rotating, nonlocal semiconductor media subjected to pulsed laser beam. The novelty of this work lies in formulating a new coupled dynamic model that integrates photothermal, mechanical stresses and carrier density with temperature interactions in an elastic semiconductor medium. The resulting coupled system for temperature, displacement, stress, and plasma density is solved using the normal-mode technique under pulsed laser beam. Numerical simulations are carried out for Silicon material to explore the influence of the electro-magnetic field and rotation. Results show that lowering the rotation produces slower thermal decay and enhanced oscillations in displacement components, reflecting long-memory heat transport at the Nano scale. Electro-magnetic field significantly modifies temperature profiles and stress amplitudes, with stronger effects near the heated surface. Rotation affect wave dispersion, while the electro-magnetic field interaction governs energy absorption and stress localization. The research presents, for the first time, electro-magnetic field photo thermoacoustic formulation for rotating semiconductors with temperature-dependent conductivity. The model enriches the theoretical understanding of ultrafast laser–matter interactions, offering guidance for the design of semiconductor devices and MEMS sensors, diagnostics operating under rapid or high-intensity thermal loads. The results are represented graphically to assess the influences of the rotation and electro-magnetic field on the plasma, thermal, and elastic waves.
Copyright (c) 2026 Ahamd .F. Al-Hazaemh, Abdel M. Abd-Alla, Salah E. Abbas, Kawther K. Alarfaj (Author) https://creativecommons.org/licenses/by/4.0
Green–CAS Wavelet Schemes with Fast Algorithms for Generalized Nonlinear Time–Space Fractional Partial Differential Equations
This study aims to acquire numerical schemes to detect the numerical solutions of fractional partial differential equations of arbitrary order, subject to prescribed initial and boundary conditions. This novel approach, referred to as the Green-CAS technique, integrates Green’s function with CAS wavelets to construct an efficient and systematic computational framework. The present approach is not only simple and easy to implement due to the Green function, but it also eliminates the need for operational matrices for boundary conditions. To further enhance computational efficiency, a fast algorithm is coupled with the Green-CAS wavelets, enabling effective handling of fractional partial differential equations. While tackling the nonlinear fractional partial differential equation of arbitrary order, the Picard iterative method is employed to transform the equation into a sequence of linear problems, which are then solved using the proposed techniques. Moreover, the order of convergence for two parameters has also been demonstrated in the convergence analysis, which further strengthens the effectiveness of the proposed technique. To show the validity and accuracy of the recommended techniques, the acquired outcomes are compared with the conventional CAS wavelets and various other renowned techniques. In addition, the results of various applications are presented in the form of graphics and tables, which elaborate on the effectiveness and correctness of the discussed method.
Fractional partial differential equations (FPDEs)
Copyright (c) 2025 Muhammad Ismail, Bongsoo Jang (Author) https://creativecommons.org/licenses/by/4.0
Improvement of the Population Mean Using Cosine Robust Regression Estimator
This paper introduces a novel family of cos-robust regression-type estimators along with special members to estimate the finite population mean under SRSWOR. The new family of estimators is produced by hybridizing the auxiliary information with the cos function. To reduce the impact of outliers, various robust regression techniques, namely Huber’s M- estimation, Mallows’ GM-estimation, Schweppe’s GM-estimation, and SIS GM-estimation, are employed and theoretically compared with the Ordinary Least Squares (OLS) method. Simulated and actual data are used to generate and validate theoretical properties, such as bias and Mean Square Error (MSE). According to the findings, the robust estimators perform better than the conventional OLS approach in terms of MSE and PRE. Mathematics Subject Classification (2020). 62D05,62G05, 62G35, 62J05
Copyright (c) 2026 Muhammad Ijaz, Muneeba Slaeem, Sadiah M. Aljeddani (Author) https://creativecommons.org/licenses/by/4.0
On Recovering a Time-dependent Inverse Problem in the Diffusion Model with a Dirichlet-type Constraint and an Integral Overposed Condition: Theory and Simulation
Our aim in this paper is to recover a time-dependent source term, along with the solution of the diffusion equation, by using a new definition of the derivative, known as the conformable approach. Herein, the inverse problem is utilized subject to Dirichlet boundary constraint conditions and an integral overposed condition. An explicit solution in series form for the considered inverse source problem is obtained by employing the Fourier expansion scheme. The thoughtful mathematical structure, including the theoretical (existence, stability, and uniqueness) for the suggested regular solution, is settled and affirmed. Two time-conformable diffusion equation examples are considered to show the stability result. Various graphical plots and numerical tables are utilized to confirm the results discussed. The final remarks, highlights, and some focused references are given at the end.
Copyright (c) 2025 Smina Djennadi, Omar Abu Arqub, Marwan Abukhaled (Author) https://creativecommons.org/licenses/by/4.0
Discrete Poisson Ramos–Louzada Exponential Distribution with Mathematical Properties, and Applications
A new two-parameter mixed Poisson distribution is introduced and explored in this study. The new model is named the Poisson Ramos Louzada Exponential distribution. Various statistical characteristics of the new count distribution are derived and studied, including moments, generating function, overdispersion, failure rate, reversed hazard function, cumulative hazard function, Mills ratio, odd function, and order statistics. A novel regression model is also introduced based on this distribution. The parameters of the new probability model are estimated using the maximum likelihood estimation approach. The estimation behaviour of these derived estimators is studied using a Monte Carlo simulation study. The flexibility and adaptability of the new distribution have been confirmed using two datasets related to radiation and corn borer. It is revealed that the proposed distribution provides efficient results are competitive count models.
Copyright (c) 2025 Abdullah M. Alomair, Muhammad Ahsan-ul-Haq (Author) https://creativecommons.org/licenses/by/4.0
Numerical Computation of Solutions and Truncation Error for Stochastic Differential Equations of Order 1.5
A recent study proposed a groundbreaking pathwise approximation method for numerically solving stochastic differential equations (SDEs) driven by Brownian motions. This approach eliminates the necessity of simulating stochastic Itˆo integrals, denoted by Jα. Instead, these integrals are replaced with random variables that maintain the same moments under the linear term condition. The main objective of this method is to deliver approximate solutions with an error rate of O(h3/2). This level of precision significantly exceeds the strong error rates achieved by the Euler and Milstein methods, which are O(√h) and O(h), respectively, where h represents the step size. The development of this method relies on the assumption that the diffusion process is nondegenerate and incorporates the Itˆo-Taylor expansion alongside a modified perturbation approach. In this paper, we demonstrate that the scheme achieves strong convergence in the Wasserstein distance with an order of O(h3/2) by leveraging techniques from the optimal transport theory
Copyright (c) 2025 Yazid Alhojilan (Author) https://creativecommons.org/licenses/by/4.0
Approximate solution for the fractional Riccati/Logistic differential equations employing the β-Khalouta decomposition technique
We provide an approximation solution to the Riccati/Logistic differential equations (RDE/LDE) with the Caputo-Katugampola fractional derivative. The proposed methodology relies on the β Khalouta decomposition method (β-KDM). The proposed approach integrates the β-Khalouta transform method with a decomposition technique. The stability study encompasses the uniqueness, convergence, and error estimation of the proposed scheme. The residual error function is computed and utilized as a fundamental criterion for assessing the accuracy and efficiency of the specified numerical method. We employ the exact solution and the fourth-order Runge-Kutta method for comparison with the results obtained from the employed method. The results confirm that the used method is a straightforward and efficient instrument for the numerical simulation of these models. Illustrative models are provided to validate the efficacy and utility of the suggested approach. MSC 2000: 26A33; 34A08; 65N06; 65N12.
Caputo-Katugampola fractional derivative
Copyright (c) 2025 Mohamed Meabed Khader, Khaled Lotfy, Asim Alawfi, Mohamed Adel (Author) https://creativecommons.org/licenses/by/4.0