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

Abstract

This manuscript explains the approximate controllability of \(\psi\)-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.