A new kind of fractional implicit sweeping processes with history-dependent operators: Well-posedness and applications

Abstract

We study the well-posedness (existence and uniqueness of a solution) to state-dependent and state-independent Caputo–Katugampola fractional implicit sweeping processes with history-dependent operators in a real Hilbert space. First, using convex analysis tools we reduce these two types of sweeping processes to equivalent differential equations. Second, we employ the Banach fixed-point theorem and fixed-point argument for condensing mappings to examine the well-posedness of the latter equations. Third, we apply our results to circuit models that incorporate memristors and fractional capacitors, and conduct some numerical simulations for these models. We note that the results in this article extend the research of Adly and Haddad (2018), Migórski et al. (2019) and Jourani and Vilches (2019).