A coupled problem described by time-dependent subdifferential operator and non-convex perturbed sweeping process

The aim of the present paper is to state well-posedness a new dynamical system driven by differential inclusion involving time-dependent subdifferential operators with integral perturbation and non-convex perturbed sweeping process. current study motivated recent works on integro-differential processes systems coupled inclusions (involving maximal monotone operators). In our development, we proceed using discretization method, combining tools first-order evolution problems type those governed normal cone $ r $-prox regular moving sets. We establish existence result class under consideration, in context infinite dimensional Hilbert setting. This allows us deal Bolza-type problem optimal control theory.