Existence and Uniqueness Results for a Class of Nonlinear Fractional Differential Equations with Nonlocal Boundary Conditions

Abstract

In this paper, we study the existence and uniqueness of solutions for fractional dierential equations with fractional integral and Caputo fractional derivatives in boundary conditions. Our analysis relies on the Banach contraction principle, Schauder fixed point theorem and Krasnoselskii's fixed point theorem. Examples are provided to illustrate the main results.

Key words and phrases. Fractional differential equations, fractional integral, Caputo fractional derivative, Existence, Uniqueness, Fixed point theorem.

2010 Mathematics Subject Classification. 34A08, 34B15