Existence and uniqueness for Caputo fractional differential equations with integral boundary condition

Abstract

In this paper, we study nonlinear fractional differential equations involving the Caputo fractional derivative subject to an integral boundary condition. First, the exact solution of the corresponding linear problem is obtained by applying tools from fractional calculus. To prove the existence of solutions for the nonlinear case, we employ Schauder’s and Krasnoselskii’s fixed point theorems. Moreover, the uniqueness of the solution is established by using the Banach contraction principle. Finally, several illustrative examples are presented to demonstrate the applicability and effectiveness of the theoretical results.