Existence and approximate controllability of fractional evolution equations with nonlocal conditions via resolvent operators

By Pengyu Chen, Xuping Zhang, Yongxiang Li. Fractional Calculus and Applied Analysis, 2020

76 citations recorded by the source corpus.

Abstract 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.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/6d88897df8ef050c50df8f96dc0c131bbd87ee41