Nonlinear Dynamics

, Volume 60, Issue 4, pp 525–534 | Cite as

Chaotic behavior of a class of discontinuous dynamical systems of fractional-order

  • Marius-F. DancaEmail author
Original Paper


In this paper, the chaos persistence in a class of discontinuous dynamical systems of fractional-order is analyzed. To that end, the initial value problem is first transformed, by using the Filippov regularization (Filippov in Differential Equations with Discontinuous Right-Hand Sides, 1988), into a set-valued problem of fractional-order, then by Cellina’s approximate selection theorem (Aubin and Cellina in Differential Inclusions Set-valued Maps and Viability Theory, 1984; Aubin and Frankowska in Set-valued Analysis, 1990). The problem is approximated into a single-valued fractional-order problem, which is numerically solved by using a numerical scheme proposed by Diethelm et al. (Nonlinear Dyn. 29:3–22, 2002). Two typical examples of systems belonging to this class are analyzed and simulated.

Fractional derivative Discontinuous dynamical system Filippov regularization Differential inclusion Numerical method 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceAvram Iancu UniversityCluj-NapocaRomania
  2. 2.Romanian Institute of Science and TechnologyCluj-NapocaRomania

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