Some New Existence, Uniqueness and Convergence Results for Fractional Volterra-Fredholm Integro-Differential Equations

Abstract

This paper demonstrates a study on some significant latest innovations in the approximated techniques to find the approximate solutions of Caputo fractional Volterra-Fredholm integro-differential equations. To this aim, the study uses the modified Adomian decomposition method (MADM) and the modified variational iteration method (MVIM). A wider applicability of these techniques are based on their reliability and reduction in the size of the computational work. This study provides an analytical approximate to determine the behavior of the solution. It proves the existence and uniqueness results and convergence of the solution. In addition, it brings an example to examine the validity and applicability of the proposed techniques.

Keywords

• Modified Adomian Decomposition Method
• Modified Variational Iteration Method
• Caputo Fractional Volterra-Fredholm Integro-Differential Equation