Optimal control of nonlocal fractional evolution equations in the α-norm of order $(1,2)$

This paper investigates the optimal control for a class of nonlocal fractional evolution equations of order $\gamma \in (1,2)$ γ ∈ ( 1 , 2 ) in Banach spaces. An adequate definition of α-mild solutions is obtained and the existence, uniqueness and continuous dependence of α-mild solutions for the presented control system are also established. The existence of optimal pairs of nonlocal fractional evolution systems is also demonstrated with a view on the construction of the Lagrange problem. Finally, an example is propounded for the presentation of optimal control.