Approximate controllability results of ψ-Hilfer fractional neutral hemivariational inequalities with infinite delay via almost sectorial operators

This manuscript explains the approximate controllability of 95-Hilfer fractional neutral hemivariational inequalities (Psi-HFNHVI) with infinite delay via an almost sectorial operator. The facts related to semigroup theory, Hilfer fractional derivative (HFD), fractional calculus, the fixed point approach, and multi-valued maps are used to prove the results. Initially, we show the existence of a mild solution and exhibit that the Psi-Hilfer fractional system is approximately controllable. Further, we have provided an example.