An Existence and Convergence Results for Caputo Fractional Volterra Integro-Differential Equations

Abstract

This paper demonstrates a study on some significant latest innovations in the approximated technique to find the approximate solutions of Caputo fractional Volterra integro-differential equations. To apply this, the study uses homotopy analysis method. A wider applicability of this technique is based on their reliability and reduction in the size of the computational work. This study provides analytical approximate to determine the behavior of the solution. It proves the existence results and convergence of the solutions. In addition, it brings some examples to examine the validity and applicability of the proposed technique.

Key words and phrases. Homotopy analysis method, Caputo fractional derivative, fractional Volterra integro-differential equation, approximate solution.

1991 Mathematics Subject Classification. 65H20, 26A33, 35C10