Existence study of semilinear fractional differential equations and inclusions for multi–term problem under Riemann–Liouville operators

Abstract

In the present paper, we study the existence and uniqueness of the solution for multi–term fractional boundary value problem under Riemann–Liouville fractional operators by using Banach's fixed point theorem. Afterward, we investigate some existence results for a semilinear fractional differential inclusions multi–term problem by using some notions and properties on set‐valued maps together with classical fixed point theorems due to Leray–Schauder. The cases when the set‐valued function has convex as well as nonconvex values are considered. Finally, some examples are given to illustrate our main results.