On a coupled system of fractional compartmental models for a biological system

Abstract

In this paper, we investigate the existence of solutions for a coupled system of fractional compartmental models as differential inclusions with coupled nonlocal and integral boundary conditions, whose multivalued terms depend on lower-order fractional derivatives. By means of nonlinear alternative of Leray-Schauder type, continuous and measurable selection theorems together with Leray-Schauder degree theory, some sufficient conditions for the existence of solutions are presented, which extend some known results. Several examples are given to demonstrate the application of our main results.