A Nonlinear Integro-Differential Equation with Fractional Order and Nonlocal Conditions

Abstract

This paper deals with a nonlinear integro-differential equation of fractional order a is an element of (0, 1) with nonlocal conditions involving fractional derivative in the Caputo sense. Under a new approach and minimal assumptions on the function f, we prove the existence, uniqueness, estimates on solutions and continuous dependence of the solutions. The used techniques in analysis rely on fractional calculus, Banach contraction mapping principle, and Pachpatte's inequality. At the end, some numerical examples to justify our results are illustrated. (C)2020 L&H Scientific Publishing, LLC. All rights reserved.