On the Existence of Solutions of Multi-Term Fractional Order Volterra Integro-Differential Equations

Abstract

In this paper, the problem of multi-term fractional order Volterra integro-differential equations is considered. The multi-term fractional order derivative part of the multi-term fractional order Volterra integro-differential equations is converted to its equivalent integral equation and Schauder’s fixed point theorem is applied to establish the existence of solutions for the multi-term fractional order Volterra integro-differential equations under some mild conditions. Furthermore, examples were given to test the applicability of the proposed theorem.