Approximate Controllability of Linear Fractional Impulsive Evolution Equations in Hilbert Spaces

Abstract: In this paper, we investigate the approximate controllability of linear fractional impulsive evolution equations in Hilbert spaces. We provide a representation of solutions utilizing impulsive operators. Necessary and sufficient conditions for the approximate controllability of linear fractional impulsive evolution equations are established in terms of the impulsive resolvent operator. An example is presented to demonstrate the application of the obtained theoretical results.