Boundary value problems for fractional differential equations with nonlocal boundary conditions

Abstract

Abstract In this paper, we establish some sufficient conditions for the existence of solutions to two classes of boundary value problems for fractional differential equations with nonlocal boundary conditions. Our goal is to establish some criteria of existence for the boundary problems with nonlocal boundary condition involving the Caputo fractional derivative, using Banach’s fixed point theorem and Schaefer’s fixed point theorem. Finally, we present four examples to show the importance of these results. MSC: 34A08, 34B10.