Existence, uniqueness and stability results for fractional nonlinear Volterra-Fredholm integro-differential equations

Abstract

In this paper, we establish some new conditions for the existence and uniqueness of solutions for a class of nonlinear Caputo fractional Volterra-Fredholm integrodifferential equations with integral boundary conditions. The desired results are proved by using Banach and Krasnoselskii’s fixed point theorems. In addition, the Ulam-Hyers stability and Ulam-Hyers-Rassias stability for solutions of the given problem are also discussed. An example is presented to guarantee the validity of our results.