10.57647/mathsci.2025.1904.19

Approximate solution for the fractional Riccati/Logistic differential equations employing the β-Khalouta decomposition technique

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  • Mohamed Meabed Khader1,
  • Khaled Lotfy2,
  • Asim Alawfi1,
  • Mohamed Adel*3,
  1. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, KSA
  2. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
  3. Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, KSA

Received: 2025-11-16

Revised: 2025-11-28

Accepted: 2025-12-06

Published in Issue 2025-12-31

Copyright (c) 2025 Mohamed Meabed Khader, Khaled Lotfy, Asim Alawfi, Mohamed Adel (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Khader, M. M., Lotfy, K., Alawfi, A., & Adel, M. (2025). Approximate solution for the fractional Riccati/Logistic differential equations employing the β-Khalouta decomposition technique. Mathematical Sciences, 19(4 (December 2025). https://doi.org/10.57647/mathsci.2025.1904.19
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Abstract

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.

Keywords

  • Riccati/Logistic differential equation,
  • Caputo-Katugampola fractional derivative,
  • Khalouta transform technique,
  • Decomposition method,
  • Convergence analysis
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