Approximate controllability of fractional evolution inclusions with damping. (July 2021) - Li, Xuemei; Liu, Xinge; Tang, Meilan
Abstract: The approximate controllability of fractional evolution inclusions with damping is studied in this paper. Under a compactness assumption on the ( α, μ ) − regularized resolvent families of operators, some properties of operators associated with the regularized family are given. Next, the existence results of the system are obtained by nonlinear alternative of Leray-Schauder and Covitz and Nadler's fixed point theorem. Furthermore, we obtain a new set of sufficient conditions for the approximate controllability of fractional evolution inclusions. Finally, examples are provided to illustrate the obtained results.