Differential equations and inclusions involving mixed fractional derivatives with four-point nonlocal fractional boundary conditions

Abstract

We study a new class of boundary value problems of mixed fractional differential equations and inclusions involving both left Caputo and right Riemann Liouville fractional derivatives, and nonlocal four-point fractional boundary conditions. We apply the standard tools of the fixed-point theory to obtain the sufficient criteria for the existence and uniqueness of solutions for the problems at hand. Illustrative examples for the obtained results are also presented.