Existence results for a nonlinear fractional differential inclusion

Abstract

In this paper, we establish  some existence results for higher-order nonlinear fractional differential inclusions  with multi-strip conditions, when when the right-hand side is convex-compact as well as nonconvex-compact values. First, we use the nonlinear alternative of Leray-Schauder type.  We obtain the next result by using the well-known Covitz and Nadler's fixed point theorem for multivalued contractions. The results are illustrated by two examples.