Trajectory Controllability of Integro-Differential Systems of Fractional Order $$\gamma \in (1,2]$$ in a Banach Space with Deviated Argument

In this paper, the fractional integro-differential control system of order $$\gamma \in (1,2]$$ in a Banach space with deviated argument is considered. In order to study the trajectory controllability for the proposed control problem, the theory of fractional calculus, Gronwall’s inequality, and fractional order cosine family are used. Finally, we provide an example to illustrate our main results.