Approximate Controllability of Fractional Evolution Equations with ?-Caputo Derivative

Abstract

The primary objective of this study is to investigate the concept of approximate controllability in fractional evolution equations that involve the ?-Caputo derivative. Specifically, we examine the scenario where the semigroup is compact and analytic. The findings are based on the application of the theory of fractional calculus, semigroup theory, and the fixed-point method, mainly Schauder's fixed-point theorem. In addition, we assume that the corresponding linear system is approximately controllable. An example is provided to illustrate the obtained theoretical results.