Optimal feedback control for fractional evolution equations with nonlinear perturbation of the time-fractional derivative term

Abstract We study the optimal feedback control for fractional evolution equations with a nonlinear perturbation of time-fractional derivative term involving Caputo derivatives arbitrary kernels. Firstly, we derive mild solution in terms semigroup operator generated by resolvents and kernel from general operators establish existence uniqueness solutions systems. Then, feasible pairs applying Filippov’s theorem is obtained. In addition, Lagrange problem has been investigated.