Stability and controllability results of [formula omitted]-Hilfer fractional integro-differential systems under the influence of impulses

Abstract

This paper is devoted to exploring a new class of ψ-Hilfer fractional integro-differential systems under the influence of impulses. Using semigroup theory, fixed-point technique, and fractional calculus, we analyzed the existence and uniqueness of mild solutions. Moreover, we proved the novel stability criteria for the considered system by using the Grönwall inequality. Further, we investigated the controllability results for the proposed system by using the new piecewise control function. Finally, the main results are validated with the aid of an example.