We investigate a specific category of perturbed sweeping processes characterized by a fractional Caputo-type derivative in Hilbert spaces, conveyed by Our study presents results on existence and uniqueness. More specifically, we utilize a method founded on rigorous reasoning to demonstrate the existence of the fractional sweeping process. This approach continues to draw on the fundamental principles of J. J. Moreau’s catching-up algorithm. In this context, we design a modified catching-up algorithm suited to the fractional framework, facilitating the generation of a sequence of approximate solutions. These theoretical results are supported by numerical simulations. For the numerical solution of our problem, we begin by presenting the method used. Then, we implement the algorithm introduced in the proof of the existence and uniqueness result to obtain approximate solutions to the studied problem.
