Trajectory controllability of fractional differential systems of order $$\alpha \in (1,2]$$α∈(1,2] with deviated argument

Abstract

In this paper, we consider a control system governed by the fractional differential equation of order $$\alpha \in (1,2]$$ with deviated argument in a Banach space X. We used the strongly continuous $$\alpha $$-order cosine family of linear operators and Gronwal’s inequality to study the trajectory controllability of the system. Also, we study the trajectory controllability of the integro-differential equations. Finally, we give an example to illustrate the application of these abstract results.