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Approach of a Class of Discontinuous Systems of Fractional Order: Existence of Solutions

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: Marius-F. Danca

Editorial: World Scientific, International Journal of Bifurcation and Chaos, 21, p.3273–3276, 2011.


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 P¶eano like theorem for ordinary di®erential
equations of fractional order.

Cuvinte cheie: Discontinuous dynamical systems, Filippov regularization, Set-valued function, Continuous selection, Fractional ODE