Approximate Controllability of Fractional Evolution Systems with Riemann--Liouville Fractional Derivatives

Abstract

In this paper, we deal with the control systems governed by fractional evolution differential equations involving Riemann--Liouville fractional derivatives in Banach spaces. Our main purpose in this article is to establish suitable assumptions to guarantee the existence and uniqueness results of mild solutions. Under these conditions, the approximate controllability of the associated fractional evolution systems involving Riemann--Liouville fractional derivatives is formulated and proved.