Existence and Uniqueness of Mittage-Leffler-Ulam Stable Solution for Fractional Integrodifferential Equations with Nonlocal Initial Conditions

Mohamed I. Abbas

Abstract

In this paper, the existence and uniqueness of mild solution for fractional integrodifferential equations with nonlocal initial conditions are investigated by using Holder’s inequality, p−mean continuity and Schauder’s fixed point theorem in Banach spaces. The Mittage-Leffler-Ulam stability results are also obtained by using generalized singular Gronwall’s inequality.

Keywords

Mild solutions, Holder’s inequality, Schauder’s fixed point theorem, The Mittage-Leffler-Ulam stability, Generalized singular Gronwall’s inequality

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