Approximate controllability of impulsive riemann-liouville fractional equations in banach spaces

Abstract

In this paper, we study control systems governed by impulsive Riemann-Liouville fractional differential equations in Banach spaces. Firstly, we introduce PC1-α-mild solutions for impulsive Riemann-Liouville fractional differential equations. Then, we make a set of assumptions to guarantee the existence and uniqueness of mild solutions. Finally, approximate controllability of the associated impulsive Riemann-Liouville fractional evolution control systems is also formulated and proved.