Pengyu Chen, Kaibin Zhang, and Yanli Xi. Approximate Controllability of Fractional Evolution Equations Via Solution Operators. Dynamic Systems and Applications 29 (2020), No. 2, 367-382

https://doi.org/10.46719/dsa202029212

ABSTRACT.
In this article, we are concerned with the approximate controllability for a class of
fractional evolution equations in Banach spaces. Sufficient conditions of approximate controllability for the desired problem are presented by constructing a control function involving Gramian controllability operator. The discussions are based on Schauder 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.

AMS (MOS) Subject Classification. 26A33; 34K37; 35R11; 93B05.