EXISTENCE, UNIQUENESS AND STABILITY RESULTS FOR FRACTIONAL NONLINEAR VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

EXISTENCE, UNIQUENESS AND STABILITY RESULTS FOR FRACTIONAL NONLINEAR VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

A. Hamoud, M. Osman

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Abstract

In this paper, we establish some new conditions for the existence and unique- ness of solutions for a class of nonlinear Caputo fractional Volterra-Fredholm integro- di erential equations with integral boundary conditions. The desired results are proved by using Banach and Krasnoselskii's  xed 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.

Keywords

Fractional Volterra-Fredholm integro-di erential equation, Caputo sense, Generalized Ulam stability, Fixed point method.