Existence results for a -Hilfer-type fractional Langevin differential inclusion

Abstract

In this paper we deals with the existence of solution for a new kind of Langevin inclusion involving -Hilfer fractional derivative. The suggested study is based on some basic definitions of fractional calculus and multivalued analysis. The existence result is obtained by making use of the nonlinear alternative of Leray-Schauder type. In the end, we are giving an example to illustrate our results.