An Iterative Algorithm to Approximate the Solution of Fractional Two-Dimensional Nonlinear Functional Integral Equations in a Banach Space

Darvishi Khezri, Samaneh; Rabbani, Mohsen; Arab, Reza; Dadashi, Vahid

doi:10.22034/cmde.2025.68614.3330

An Iterative Algorithm to Approximate the Solution of Fractional Two-Dimensional Nonlinear Functional Integral Equations in a Banach Space

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematics, Sar. C., Islamic Azad University, Sari, Iran.

10.22034/cmde.2025.68614.3330

Abstract

This study investigates the solvability and approximation of fractional two-dimensional nonlinear functional integral equations in a Banach space. Motivated by the increasing relevance of fractional models in nonlinear sciences—including diffusion, viscoelasticity, and nonlinear wave propagation—we establish new existence results using a generalized Darbo fixed-point theorem combined with the measure of noncompactness. To validate the theory, an iterative Sinc-interpolation algorithm is developed, achieving exponential convergence for numerical approximation. The proposed approach not only generalizes existing one-dimensional results to higher dimensions but also provides a practical framework for analyzing soliton-type and other localized nonlinear structures in fractional systems. Numerical experiments confirm the accuracy and effectiveness of the method.

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