Abstract
Of concern are the existence and approximate controllability of fractional differential equations governed by a linear closed operator which generates a resolvent. Using the analytic resolvent method and the continuity of a resolvent in the uniform operator topology, we derive the existence and approximate controllability results of a fractional control system.
Highlights
We are concerned with the approximate controllability for a fractional differential equation of the form
We can prove the continuity of a resolvent in the uniform operator topology and the compactness of the solution operator in the case of an analytic resolvent
We study approximate controllability of fractional control system ( . ) by using the analytic resolvent method and the uniform continuity of the resolvent
Summary
We are concerned with the approximate controllability for a fractional differential equation of the form We can prove the continuity of a resolvent in the uniform operator topology and the compactness of the solution operator in the case of an analytic resolvent. In Section , we recall some definitions of Caputo fractional derivatives, analytic resolvent, mild solutions to equation
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