Computational Methods, Existence and Uniqueness for Solving 2-D Fractional Nonlinear Fredholm Integro-Differential Equation

Authors

  • Abeer Albugami Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
  • Nuha A. Alharbi Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
  • Amr M. S. Mahdy Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5924

Keywords:

TDFNFI-DE, existence and uniqueness, ADM, HAM

Abstract

In this paper, we have investigated the two-dimensional fractional nonlinear Fredholm integro-differential equation (TDFNFI-DE). These equations are used in many fields, including particle dynamics in physics, biology, and control theory. We have developed an effective combined approach in our work that uses Homotopy analysis (HAM) and the Adomian decomposition method (ADM) to solve fractional integro-differential equations in two dimensions. Numerical experiment results show the effectiveness of our recently created technique. We prove the existence and uniqueness of the exact solution. To illustrate the numerical effectiveness of the suggested approach, we provide a number of numerical examples. The suggested approach is accurate and applicable to various nonlinear issues in science, according to theoretical and numerical results.

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Mathematical Analysis

License

Copyright (c) 2025 Abeer Albugami, Nuha A. Alharbi, Amr M. S. Mahdy

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How to Cite

Computational Methods, Existence and Uniqueness for Solving 2-D Fractional Nonlinear Fredholm Integro-Differential Equation. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5924. https://doi.org/10.29020/nybg.ejpam.v18i2.5924