APPROACH OF A CLASS OF DISCONTINUOUS DYNAMICAL SYSTEMS OF FRACTIONAL ORDER: EXISTENCE OF SOLUTIONS

Abstract

In this paper, we are concerned with the possible approach to the existence of solutions for a class of discontinuous dynamical systems of fractional order. To this purpose, the underlying initial value problem is transformed into a fractional set-valued problem. Next, Cellina's Theorem is applied leading to a single-valued continuous initial value problem of fractional order. The existence of solutions is assured by a Péano-like theorem for ordinary differential equations of fractional order.