A discussion concerning to partial-approximate controllability of Hilfer fractional system with nonlocal conditions via approximating method

Abstract

This study focuses on the partial-approximate controllability of Hilfer fractional differential evolution equations in Hilbert spaces. We give the approximate problem of the control system and obtain the compactness of the approximate solution set using fractional calculus, the variational approach, and the approximate technique. Finally, an example is provided to illustrate our abstract results to the partial-approximate controllability of the semilinear system.