A coupled fractional conformable Langevin differential system and inclusion on the circular graph

Abstract

In this paper, we study a class of coupled fractional conformable Langevin differential system and inclusion on the circular graph. On the one hand, the existence and uniqueness of solutions of this coupled fractional conformable Langevin differential system are studied by fixed point theorems. On the other hand, in the multivalued case, the existence of at least one solution of the fractional conformable Langevin differential inclusion on the circular graph is discussed and the sufficient conditions are established by using Leray–Schauder nonlinear alternative and Covitz–Nadler fixed point theorem.

Keywords

• circular graph
• fractional conformable derivative
• Langevin differential equation and inclusion
• fixed point theorem