Approximate controllability of impulsive neutral fractional hemivariational inequalities involving memory term

Abstract

This paper develops a new analytical framework for impulsive neutral fractional differential systems with memory terms. Fractional calculus is adopted for its superior capability in capturing hereditary and memory effects commonly observed in complex dynamical systems. To effectively describe the nonlinear and nonsmooth behavior of the system, the theory of hemivariational inequalities is incorporated. Moreover, history-dependent operators are introduced to explicitly account for the influence of past states on the present dynamics and future evolution of the system. The main objectives of this study are twofold. First, we establish the existence of solutions for the considered impulsive neutral fractional differential systems by employing techniques from fixed-point theory, fractional calculus, and the generalized Clarke subdifferential. Second, we analyze the controllability of the system, with an emphasis on steering the system between prescribed states within a finite time horizon.