A class of fractional delay nonlinear integrodifferential controlled systems in Banach spaces

We study a class of fractional delay nonlinear integrodifferential controlled systems associated with analytic semigroup in Banach spaces. Existence of α-mild solutions and optimal controls are obtained. Lastly, an example is presented to illustrate our abstract results.

Research highlights► Fractional delay nonlinear integrodifferential controlled system via analytic semigroup is studied. ► Existence result for α-mild solutions is shown. Existence result for Lagrange type optimal controls problem is presented.