Exact controllability and continuous dependence of solution of a conformable fractional control system

The exact controllability of a conformable fractional differential system is established in this paper. The system is described by a non-densely defined linear part satisfying the Hille Yosida condition, and a control term appearing in the nonlinear part. The existence of mild solution and exact controllability is proved by Banach fixed point theorem for the system with non-local conditions and deviated argument. The continuous dependence of the mild solution is also studied. An example is discussed to illustrate the results.

Keywords:

Non-dense operator , Deviated Argument , Non-local conditions , Conformal fractional differential equation , Controllability