Approximate controllability of fractional semilinear control system of order $\alpha\in (1,2]$ in Hilbert spaces

Abstract

The objective of this paper is to present some sufficient conditions for approximate controllability of fractional order semilinear system of order $\alpha\in(1,2]$ in Hilbert spaces. The results are obtained by using Schauder's fixed point theorem. At the end, an example is given to show the effectiveness of the result.