Solving a Class of Volterra Integral Equations With M-Derivative

Ilie, Mousa; Khoshkenar, Ali; Torabi Giklou, Asadollah

doi:10.22034/cmde.2024.58936.2498

Solving a Class of Volterra Integral Equations With M-Derivative

Document Type : Research Paper

Authors

¹ Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.

² Department of Basic Sciences, Parsabad Moghan Branch, Islamic Azad University, Parsabad Moghan, Iran.

10.22034/cmde.2024.58936.2498

Abstract

This article presents the development and analysis of the M-fractional Neumann method (MFNM) for solving a class of time M-fractional Volterra integral equations. The MFNM is based on the well-known Neumann method and is shown to provide efficient solutions for the considered equations. The proposed approach's existence, uniqueness, and convergence are studied using several theorems. The results demonstrate the MFNM's effectiveness in solving time M-fractional Volterra integral equations. Numerical examples are provided to illustrate the capabilities and adequacy of the MFNM for a class of fractional integral equations.

Keywords