Existence and Approximate Controllability of Fractional Evolution Equations with Nonlocal Conditions Via Resolvent Operators - Chen, Pengyu; Zhang, Xuping; Li, Yongxiang (Fractional calculus & applied analysis, 2020)
In this article, we are concerned with the existence of mild solutions as well as approximate controllability for a class of fractional evolution equations with nonlocal conditions in Banach spaces. Sufficient conditions of existence of mild solutions and approximate controllability for the desired problem are presented by introducing a new Green’s function and constructing a control function involving Gramian controllability operator. The discussions are based on Schauder’s fixed point theorem as well as the theory of α -order solution operator and α -order resolvent operator. An example is given to illustrate the feasibility of our theoretical results.