Communications in Nonlinear Analysis (CNA) is an international peer-reviewed quarterly publication that publishes high-quality papers on all aspects of Energy and Sustainability. CNA is an open access publication, The following manuscript format can be published in the journal: Original article, short communication (brief report or brief communication), review article, systematic review and meta-analysis, Letter to editor, commentary, and editorial. Financial Policies Article Processing Charges Research & Science Group has supported all the publishing costs of Communications in Nonlinear Analysis (CNA), article processing charge and any other publication fees in the journal are free for authors. Subscription Fee Communications in Nonlinear Analysis (CNA) has published as an open-access electronic journal, so there is no subscription fee for audiences. Open Access Policies CNA is licensed under the terms of the Creative Commons Attribution License 4.0 International (CC-BY 4.0). Licensees may copy, distribute, display and make derivative works only if they cite the original published CNA article. Publication Policies CNA is following of Committee on Publication Ethics (COPE) and complies with the highest ethical standards in accordance with ethical laws. Copyright Notice Authors who publish with this journal agree to the following terms: Authors retain copyright and grant the journal right of first publication, with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal. Authors are able to enter into separate, additional contractual arrangements for the nonexclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
Fixed point theorems of some mappings in n-Banach spaces
In the present article, we introduce Meir-Keeler contraction mappings and C´ iric´ contraction mappings on n-Banach spaces. In particular, we discuss the existence and uniqueness of a fixed point of such mappings in an n-Banach space. On the other hand, we introduce Hardy-Rogers contraction mappings on an n-Banach space. In particular, we prove the existence and uniqueness of a fixed point of such a mapping in an n-Banach space. However, several results are demonstrated on fixed point theorems of some mappings in a nonempty, closed and bounded subset with respect to n linearly independent vectors of an n-Banach space.
Copyright (c) 2025 Jawad Ettayb (Author) https://creativecommons.org/licenses/by/4.0
Benefaction of Rothe's Time Discretization Method to Solve Diffusion Equation Involving Riemann-Liouville Fractional Integral and Delay Integral Function
This paper presents a diffusion equation involving $\alpha^{th}$ order Riemann-Liouville (R-L) fractional integral along with integral forcing function for delay and some constant coefficients. We apply $L2$ scheme to discretize the fractional integral function and Rothe's method is opted to establish the existence and uniqueness of a strong solution. In addition, we provide some error estimation and continuous on initial data. Eventually, we provide an application to manifest the results.
Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
Analysis of Fractional Gas Dynamic Equations Using Atangana-Baleanu Derivative Operator
This paper presents approximate analytical solutions for solving the nonlinear homogeneous and non-homogeneous gas dynamics equations with the Atangana-Baleanu fractional derivative operator. The validity of the solutions is verified by providing existence and uniqueness criteria for the solution using the employed technique. To illustrate the ability and efficiency of the method, absolute errors, tables, and graphical presentations of numerical solutions for specific cases are obtained.
Copyright (c) 2025 Bhausaheb R. Sontakke, Shankar R. Raut (Author) https://creativecommons.org/licenses/by/4.0
Automated Phishing Detection Through URL Analysis and Machine Learning
Phishing attacks are categorized as one of the greatest threats to cybersecurity. They are a form of misinfor-mation designed to make users provide important and personal information via fake websites or emails. This paper realizes the notion of a machine learning-based phishing detection tool aimed at classifying URLs as ”phishing,” ”suspicious,” or ”safe.” Utilizing a Random Forest classifier, the system examines URL-based characteristics, including URL length, special symbols, and the usage of HTTPS to distinguish between real URLs and fake ones (phishing URLs) with high accuracy. The model was trained and validated on a dataset of labeled URLs, achieving 95.2% classification accuracy, which is higher compared to other results. For the sake of usability, the detection tool is implemented as a web application for real-time classification with a user-friendly interface. The performance is evaluated using metrics such as accuracy, precision, recall, and F1-score to assess effectiveness. This paper helps to improve the level of online security by providing an automated approach that reduces dependence on human judgment and can efficiently detect phishing threats.
On Erdos-Lax Inequality for the Class of Composite ˝ Polynomials
Copyright (c) 2025 Bashir Ahmad Ganie, Varun Mohan, Khursheed Alam, Department of Mathematics, Government Degree College Drass, Kargil, 194102, India (Author) https://creativecommons.org/licenses/by/4.0
Asymptotic Representations of Hypergeometric Bernoulli Polynomials of Order 2 Inside Regions Related to the Roots of e^w − 1 − w = 0
Copyright (c) 2026 https://creativecommons.org/licenses/by/4.0
A Novel Approach in Elastic Flight Simulation of a Slender Flexible Vehicle to Assess the Role of Thrust Deviations in ‎Stability
Because of the linearized and simplified models, many of the existing methods for stability analysis cannot accurately simulate the real flight behavior of the flexible vehicles, so non-linear models with minimum simplification should be employed instead. However, due to the need to simultaneously solve ‎coupled complex structural ‎and aerodynamic equations in each time step, such models require massive calculations, ‎greatly reducing the simulation speed and increasing the run ‎time. In this research, the volume of computations in each time step was reduced by appropriate lookup ‎tables made from some pre-performed calculations, and as a result, a higher execution speed ‎of the simulation was achieved. With this new strategy, the role of various design inputs, such as structure stiffness, which is usually represented by the natural frequency, exerted maneuvering acceleration, propulsion force function, and roll speed on trajectory, collision accuracy, and flight stability of a flexible projectile can be achieved. Only the role of thrust function and structure flexibility has been addressed in this research. The results show that the ‎‎inherent inaccuracies in the thrust force (inherent deviation and out-centering) and ‎reduction of the ‎natural frequencies increase the effect of aeroelasticity and the probability of the flight instability of the projectile in ‎open-loop flights. General (Classic) flight simulations often neglect elastic properties, which can sometimes result in significant errors. Taking the aeroelasticity into account would result in massive calculations and computational time costs, on the other hand. This paper makes the simulation velocity much faster (to somehow close to a rigid projectile simulation) by using some pre-prepared look-up tables from existing aeroelastic run-time computations. This method has not been employed in similar aeroelastic calculations reported in the literature.
Copyright (c) 2025 Hossein Faveadi, Ali R. Davari, Farshad Pazooki, Majid Pouladian (Author) https://creativecommons.org/licenses/by/4.0
A Unified Framework for Interval-Valued Fuzzy Multi-Criteria Decisions: Synergizing Dynamic Outranking and Aggregation-Based Methods
Contemporary decision-making is increasingly confronted with complex, uncertain environments where traditional multi-criteria decision-making (MCDM) models, reliant on precise data, prove inadequate. While interval-valued fuzzy sets (IVFS) provide a sophisticated mechanism for capturing linguistic vagueness and expert doubt, existing IVFS-based MCDM methods often suffer from rank instability, sensitivity to subjective parameters, and insufficient adaptability to dynamic uncertainty. To bridge these critical gaps, this article introduces a novel unified framework for Interval-Valued Fuzzy MCDM (IVF-MCDM) that synergistically integrates the strengths of dynamic outranking relations and robust aggregation-based techniques. The framework is operationalized through two innovative hybrid methodologies: first, an enhanced ELECTRE I model employing Type-2 interval-valued fuzzy sets with adaptive, data-driven concordance and discordance indices that dynamically adjust to uncertainty levels; and second, a symmetrical Interval-Valued Fuzzy Weighted Aggregated Sum Product Assessment (IVF-WASPAS) approach that balances additive and multiplicative aggregation logics through a symmetry principle to enhance ranking stability. The practical efficacy, robustness, and superior performance of the proposed unified framework are rigorously validated through comprehensive case studies in strategic healthcare system evaluation and sustainable urban landfill site selection. Comparative analyses with standalone methods such as IVF-TOPSIS and IVF-COPRAS demonstrate significant improvements in reliability, reduced rank reversal, and enhanced handling of pervasive uncertainty. This research contributes a methodologically sound, versatile decision-support tool that advances the theoretical frontier of fuzzy MCDM and offers practitioners in engineering, management, and policy a powerful instrument for navigating complex, ambiguous strategic landscapes.
Copyright (c) 2025 Faezeh Jokar, Mohammad Jalali Varnamkhast (Author) https://creativecommons.org/licenses/by/4.0
Some common fixed point theorems for single valued mappings in G-ultrametric spaces
The purpose of this paper is to prove some common fixed point theorems for a single valued stronglycontractive mapping having a pair of maps on a spherically complete G-ultrametric space. c ⃝2016 All rightsreserved.
spherically complete G-ultrametric space
Generalized Monotone Method for System of Riemann-Liouville Fractional Reaction-Diffusion Equations
In this paper, our aim is to obtain the integral representation for the solution of linear Riemann-Liouville reaction-diffusion equations of order $q$ in terms of Green's function where $ 0<q<1 .$ We have developed a generalized monotone method for non-linear weakly coupled system of Riemann-Liouville reaction-diffusion equations when the forcing term is the sum of increasing and decreasing functions. The generalized monotone method yields monotone sequences which converges uniformly and monotonically to coupled minimal and maximal solutions. Under uniqueness assumption, we proved the existence of a unique solution for the non-linear system of Riemann-Liouville reaction-diffusion equations.
Algorithm for Equations of Hammerstein Type and Applications
Equations of Hammerstein type cover large variety of areas and are of much interest to a wide audience due to the fact that they have applications in numerous areas. Suitable conditions are imposed to obtain a strong convergence result for nonlinear integral equations of Hammerstein type with monotone type mappings. A technique which does not involve the assumption of existence of a real constant whose calculation is unclear has been used in this study to obtain the strong convergence result. Moreover, our technique is applied to show the forced oscillations of finite amplitude of a pendulum as a specific example of nonlinear integral equations of Hammerstein type. Numerical example is given for the illustration of the convergence of the sequences of iteration. These are done to demonstrate to our readers that this approach can be applied to problems arising in physical systems.
Fixed points of Nesic type contraction maps in Convex metric spaces
We define Nesic type contraction maps in convex metric spaces and prove the existence and uniqueness of fixed points of these maps in convex metric spaces. Our results extend the results of Nesic ([1], Results on fixed points of asymptotically regular mappings ) from the metric space setting to convex metricspaces.
Measures of Noncompactness on Ω-distance Spaces.
. The aim of this article is to present a new framework for studying measures of noncompactness in G-metric spaces. First, we introduce the concept of Ω-distance space as an Ω-measure of non-compactness on G-metric spaces. Finally, we use our main result to characterize G-metric completeness.
SOME LP− TYPE INEQUALITIES FOR POLAR DERIVATIVE OF A POLYNOMIAL
In this paper, we shall prove some Lpinequalities for the polar derivative of a polynomial having zerosin |z| ≤ k ≤ 1 and thereby obtain generalizations and refinements of an integral inequality due to Barchand Charamet al
Strong Convergence of Monotone Hybrid Algorithms for Maximal Monotone Mappings and Generalized Nonexpansive Mappings
A class of generalized nonexpansive mappings in Banach spaces is considered and a new monotone hybrid algorithm is presented for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a generalized nonexpansive mapping. Under certain conditions on the associated parameters, a strong convergence result is established. Moreover, the obtained result is applied to prove a strong convergence theorem for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a generalized nonexpansive mapping in a Hilbert space.
Existence and Uniqueness Solutions of System Caputo-type Fractional-Order Boundary Value Problems Using Monotone Iterative Method
In this paper, we investigate the existence and uniqueness solutions of nonlinear boundary value problems for system of Caputo type nonlinear fractional differential equations of the form:\begin{equation*}\label{*}\left\{\begin{array}{c} ^cD_{a^{+}}^{q;\psi} u_{i}(t)=F_{i}(t,u_{1}(t),u_{2}(t)) \quad t\in J=[a,b],\\ \phi(v_{i}(a),v_{i}(b))=0. \end{array} \right. \end{equation*}\\ To develop a monotone iterative technique by introducing upper and lower solutions to Caputo type fractional differential equations with nonlinear boundary conditions. The monotone method yield monotone sequences which converges to uniformly and monotonically to extremal solutions.
Keyword: Riemann-Liouville fractional derivative
The Solutions of Systems of Rational Difference Equations in Terms of Fibonacci Numbers
In this paper, we get the form of the solutions of the following difference equation systems with nonzero real numbers initial conditions z(n+1) =w(n)(z(n-4) + w(n-5))/w(n-5) + z(n-4) - w(n),w(n+1) =z(n-3)(z(n-3) + w(n-4)/2z(n-3) + w(n-4).z(n+1) =w(n)(w(n-5) -z(n-4))/w(n-5)- z(n-4) + w(n),w(n+1) =z(n-3)(w(n-4) -z(n-3)/w(n-4)
Investigating a Coupled System with Riemann-Liouville Fractional Derivative by Modified Monotone Iterative Technique
In recent time, the area of arbitrary order differential equations (AODEs)has been considered very well. Different aspects have been investigated for the saidarea. One of the important and most warm area is devoted to study multiplicityresults along with existence and uniqueness of solutions for the said equations. In thisregard various techniques have been utilized to investigate the said area. Monotoneiterative technique (MIT) coupled with the method of extremal solutions has beenused recently to investigate multiplicity of solutions to some AODEs. In this researchwork, we deal a coupled system of nonlinear AODEs under boundary conditions (BCs)involving Riemann-Liouville fractional derivative by using fixed point theorems dueto Perov’s and Schuader’s to study existence and uniqueness results. Using Perove’sfixed point theorem ensures uniqueness of solution to systems of equations, whileexistence of at least one solution is achieved by Schauder’s fixed point theorem.Then we come across the multiplicity of solutions and establish some criteria for theiterative solutions via using updated type MIT together with the method of upper andlower solutions for the considered system of AODEs. Corresponding to multiplicityresults of solutions, we first establish two sequences of extremal solutions. One of thesequence is monotonically decreasing and converging to lower solution. On the otherhand, the other sequence is monotonically increasing and converging to the uppersolution. In last we give suitable examples to illustrate the main results.
Perov’s and Schuader’s fixed point theorems
Convergence of an M-step Iteration Scheme to the Commo Fixed Points of Finite Family of Mixed-Type Total Asymtotically Nonexpansive Mappings in Uniformly Convex Banach Spaces
We propose an m-step iteration scheme of hybrid mixed-type for m-total asymptotically nonexpansive self mappings and m-total asymptotically nonexpansive nonself mappings and establish some weak convergence theorems of the scheme to the common fixed point of the mappings in the setting of uniformly convex Banach spaces. In additon, we proved demiclosedness principle for total asymptotically nonexpansive nonself mappings in uniformly convex Banach spaces. Our results extend and genralise the results in [23] and other numerous results currently in literature.
Total Asymptotically Nonexpansive Nonself Mapping
An Application of Fixed Point Theory to A Nonlinear Integral Equation in Banach Spaces
In this paper we propose a new iterative scheme, called the AF iteration process, for approximating the unique solution of a mixed type Volterra-Fredholm functional nonlinear integral equation. We prove in the sense of Berinde \cite{Berin} that our new iterative scheme converges at a rate faster than some of the leading iterative schemes in the literature which have been employed recently to approximate the unique solution of a mixed type Volterra Fredholm functional nonlinear integral equation. We also prove that our new iterative method converges strongly to the unique solution of a mixed type Volterra Fredholm functional nonlinear integral equation. In addition, we give data dependence result for the solution of the nonlinear integral equation which we are considering with the help of our new iterative scheme. Our results improve and unify some well known results in the existing literature.
Existence of Positive Solutions for 2n-Order Lidstone Boundary Value Problems with P-Laplacian Operator
In this paper, we establish the existence of positive solutions for $2n^{text {th}}$ order Lidstone boundary value problems with $p$-Laplacian of the form$$(-1)^n[phi_{p}(y^{(2n-2)}(t)-k^2y^{(2n-4)}(t))]''=f(t,y(t)), ~~t in [0, 1], $$$$y^{(2i)}(0)=0=y^{(2i)}(1), for $0leq i leq n-1,$ where $ngeq 2$ and $k>0$ is a constant, by applying Guo--Krasnosel'skii fixed point theorem.
Some Inequalities for the Polar Derivative of a Polynomial Having S-Fold Zeros at the Origin
Let $P(z)$ be a polynomial of degree $n$ having all its zeros in $|z|\leq 1$ then for all $(\alpha_i)^t_{i=1}\in \mathbb{C}$ with $|\alpha_i|\geq 1, 1\leq i\leq t<n$, it was proved by Jain[V. K. Jain, Generalization of an inequality involving maximum moduli of a polynomial and its polar derivative, Bull Math Soc Sci Math Roum Tome. 98, 67–74 (2007)] that\begin{align*}\max\limits_{|z|=1}|D_{\alpha_t}...D_{\alpha_2}D_{\alpha_1}P(z)|\geq\frac{n_t}{2^t}\left[A_{\alpha_t}\max\limits_{|z|=1}|P(z)|+\left( 2^t\prod\limits_{i=1}^{t}|\alpha_i|- A_{\alpha_t}\right)\min\limits_{|z|=1}|P(z)| \right].\end{align*}where $n_t=n(n-1)...(n-t+1)$ and $A_{\alpha_t}=(|\alpha_1|-1)(|\alpha_2|-1)...(|\alpha_t|-1)$. In this paper, we generalize this and some other results.
Coincidence Points with φ-Contractions in Partially Ordered Fuzzy Metric Spaces
In this paper our main result is a coupled coincidence point theorem for a compatible pairin a fuzzy metric space with a partial ordering under the assumption of a new coupled contraction inequality which involves a recently introduced control function which is a generalization ofmany such functions previously used in literatures. The proof depends on a lemma in which weprove a condition for simultaneous holding of Cauchy criteria for two sequences. We use H-typet-norms in this paper in order to utilize the equi-continuity of the t-norm iterates in the proofof the lemma. The contraction inequality also involves another function which is borrowed froma recent work, there is a partial ordering defined on the fuzzy metric space. There are severalcorollaries of the main theorem. An illustrative example is given.
Isolation Effect on Age-Stratified Compartmental Model of the COVID-19
Focusing on the dynamics of the most recent outbreak of COVID-19, we formulate an age distributed model with five different components in terms of nonlinear partial differential equations. The model has been analyzed by studying the stability of the equilibrium points and their reproduction number. To explore the disease effect on different ages more efficiently, we apply the recent estimated data in the formulated model and analyze it numerically. From the model’s numerical solution profiles, we observed more susceptibility and infection among the older population. Also studied the effectiveness of isolation in controlling illness and death.
On New Fixed Point Results for Some Classes of Enriched Mappings in N-Banach Spaces
We introduce the concepts of enriched n-contraction mapping, enriched n-Chatterjea mapping and enriched n-Kannan mapping in linear n-normed space. We prove some fixed point theorems for such mappings using Krasnoselsij iteration process in n-Banach spaces. The results presented in this paper improve the recent works of Berinde and Pacurar (J. Fixed Point Theory Appl. (2020) 22-38), Berinde and Pacurar (Preprint, arXiv:1909.03494) and Berinde and Pacurar (Preprint, arXiv:1909.02379, 2019) to linear n-normed spaces.
Convergence Theorems for Monotone Generalized α-Nonexpansive Mappings in Ordered Banach Space by a New Four-Step Iteration Process with Application
We introduce a new four-step iterative algorithm and show that the new algorithm converges faster than a number of existing iterative algorithms for contraction mappings. We prove strong and weak convergence results for approximating fixed points of monotone generalized α-nonexpansive mappings. Further, we utilize our proposed algorithm to solve Split FeasibilityProblem (SFP). Our result complements, extends and generalizes some existing results in literature.
A Split Common Fixed Point and Null Point Problem for Lipschitzian Quasi Pseudocontractive Mappings in Hilbert Spaces
A split common fixed point and null point problem (SCFPNPP) which includes the splitcommon fixed point problem, the split common null point problem and other problems related to the fixed pointproblem and the null point problem is studied. We introduce a Halpern--Ishikawa type algorithm for studying the split common fixed point and null point problem for Lipschitzian quasi pseudocontractive operators and maximal monotone operators in real Hilbert spaces. Moreover, we establish a strong convergence results under some suitable conditions and reduce our main result to above-mentioned problems. We give numerical result to demonstrate the convergence of our algorithms and compare rate of convergence some iterative algorithms. Finally, we applied the study to split feasibility problem (FEP), split equilibrium problem (SEP), split variational inequality problem (SVIP) and split optimization problem (SOP).
Fixed Point And Coupled Fixed Point Theorems For Multivalued Contractions With Respect To The Excess Functional
In this paper, we will consider the coupled fixed point problem for a multi-valued operator satisfying acontraction condition with respect to the excess functional in b-metric spaces. The approach is basedon a fixed point theorem for a multi-valued operator in the setting of a b-metric space. On one hand,we will consider the problem of the existence of the solutions and on the other hand, data dependence,well-posedness, Ulam-Hyers stability and limit shadowing property of the coupled fixed point problem arediscussed. Some applications to a system of integral inclusions and to a multi-valued periodic boundaryvalue problem are also given. c
multi-valued periodic boundary value problem
We introduced a new class of multi-valued mappings, called P-KKM mappings, which generalized the notationof R-KKM maps of Raj and Somasundaram [KKM-type theorem for best proximity points, AppliedMathematics Letters, 25 (2012), 496-499] and appropriate to best proximity theory. An analog version ofKKM property and a common fixed point theorem is also proved.
Convergence of general composite iterative method for infinite family of nonexpansive mappings in Hilbert spaces
In this paper by using W_n -mapping, we introduce a composite iterative method for finding a commonfixed point for infinite family of nonexpansive mappings and a solution of a certain variational inequality.Furthermore, the strong convergence of the proposed iterative method is established. Finally, some sim-ulation examples are presented. Our results improve and extend the previous results. c ⃝2016 All rightsreserved.