Efficient Numerical Solutions for Fractional Integro-Differential Equations via Conformable Differointegration and the Variational Iteration Method

Abstract

Multidimensional integro-differential equations (MDIDEs) involve equations

where an unknown function, depending on multiple variables, is subjected to

both differentiation and integration operations. These equations combine

integral and differential operators within a multidimensional framework. The

integral equation is referred to as a multidimensional fractional integro-

differential equations (MDFIDEs) when the differentiation or integration are

of fractional order. Since it is challenging to calculate these problems

analytically, the major goal of this study is to use the Variational Iteration

Method (VIM) to solve such equations by conformable fractional order

integrals and derivatives (CFOID). Beginning, A suggested method of an

iterative sequence of approximate solutions was driven, and then verify its

convergence to the exact solution in the middle of the kernel of the integro-

differential equations (IDE) under specified conditions. Two illustrated

examples, linear and nonlinear, are provided