NEW RESULTS ON CAPUTO FRACTIONAL VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

NEW RESULTS ON CAPUTO FRACTIONAL VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

A. A. Sharif , A. A. Hamoud , M. M. Hamood , K. P. Ghadle

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Abstract

This article investigates the existence and uniqueness of solutions for a nonlocal initial condition of the Caputo fractional Volterra-Fredholm integro-differential equation in a Banach space. We shall prove the existence and uniqueness of the results by using the Banach and Krasnoselskii fixed-point theorems. A number of illustrative examples will be given to further the understanding of our main conclusions.

Keywords

Volterra-Fredholm integro-differential equation, Caputo fractional derivative, Fixed point method.