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

Received (to be inserted by publisher) In this letter we are concerned with the possibility to approach the existence of solutions to a class of discontinuous dynamical systems of fractional order. In this purpose, the underlying initial value problem is transformed into a fractional set-valued problem. Next, the 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