On system of nonlinear coupled differential equations and inclusions involving Caputo-type sequential derivatives of fractional order

Abstract

We investigate a new class of boundary value problems of a nonlinear coupled system of sequential fractional differential equations and inclusions involving Caputo fractional derivatives and boundary conditions. We use standard fixed-point theory tools to deduce sufficient criteria for the existence and uniqueness of solutions to the problems at hand. Examples are discussed to illustrate the validity of the proposed results.