Existence of solutions for Caputo sequential fractional differential equations with integral boundary conditions

The purpose of this paper is to investigate the existence and uniqueness of solutions to the Caputo sequential fractional differential equations and inclusions with integral boundary conditions. When it comes to proving the existence of solutions, the Krasnoselskii's fixed point theorem is employed. Further, the Banach's contraction principle and the Leray-Schauder alternative are employed to prove the uniqueness of the results. Further, for the multi-valued case, we employ the nonlinear alternative for Kakutani maps, and Convitz and Nadler's fixed point theorem. We emphasize our results with numerical examples.

Keywords:

Fractional Differential Equations (FDEs) , Fractional Differential Inclusions , Existence , Integral boundary conditions (IBCs) , Fixed point