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

In this current article, the well-known Neumann method for solving the time M-fractional Volterra integral equations of the second kind is developed. In the several theorems, existence and uniqueness of the solution and convergence of the proposed approach are also studied. The Neumann method for this class of the time M-fractional Volterra integral equations has been called the M-fractional Neumann method (MFNM). The results obtained demonstrate the efficiency of the proposed method for the time M-fractional Volterra integral equations. Several illustrative numerical examples have presented the ability and adequacy of the MFNM for a class of fractional integral equations.

Keywords