Existence and approximate controllability of Riemann-Liouville fractional evolution equations of order 1 < μ < 2 with weighted time delay

Abstract

This article demonstrates the existence as well as the approximate controllability of semilinear fractional control systems governed by the μ∈(1,2)-order Riemann-Liouville fractional evolution equation with weighted time delay. Firstly, properties of the cosine family and the corresponding sine family are proved. Then an existence result is achieved for the concerned problem by utilizing fixed point theorem approach. The approximate controllability is also studied under essential conditions. Finally, we propose an example of the obtained abstract result.