On Nonconvex Perturbed Fractional Sweeping Processes

Abstract

This paper is devoted to the existence and uniqueness of solution for a large class of perturbed sweeping processes formulated by fractional differential inclusions in infinite dimensional setting. The normal cone to the (mildly non-convex) prox-regular moving set C(t) is supposed to have a Hölder continuous variation, is perturbed by a continuous mapping, which is both time and state dependent. Using an explicit catching-up algorithm, we show that the fractional perturbed sweeping process has one and only one Hölder continuous solution. Then this abstract result is applied to provide a theorem on the weak solvability of a fractional viscoelastic frictionless contact problem. The process is quasistatic and the constitutive relation is modeled with the fractional Kelvin–Voigt law. This application represents an additional novelty of our paper.