caa a22 4500 445362057 CHVBK 20180317142918.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s11071-010-9915-z doi (NATIONALLICENCE)springer-10.1007/s11071-010-9915-z Danca Marius-F Dept. of Mathematics and Computer Science, Avram Iancu University, 400380, Cluj-Napoca, Romania aut Numerical approximation of a class of discontinuous systems of fractional order [Elektronische Daten] [Marius-F. Danca] In this paper we investigate the possibility to formulate an implicit multistep numerical method for fractional differential equations, as a discrete dynamical system to model a class of discontinuous dynamical systems of fractional order. For this purpose, the problem is continuously transformed into a set-valued problem, to which the approximate selection theorem for a class of differential inclusions applies. Next, following the way presented in the book of Stewart and Humphries (Dynamical Systems and Numerical Analysis, Cambridge University Press, Cambridge, 1996) for the case of continuous differential equations, we prove that a variant of Adams-Bashforth-Moulton method for fractional differential equations can be considered as defining a discrete dynamical system, approximating the underlying discontinuous fractional system. For this purpose, the existence and uniqueness of solutions are investigated. One example is presented. Springer Science+Business Media B.V., 2010 Fractional systems nationallicence Discontinuous systems nationallicence Chaotic attractors nationallicence Filippov regularization nationallicence Adams-Bashforth-Moulton method for fractional differential equations nationallicence Nonlinear Dynamics Springer Netherlands 66/1-2(2011-10-01), 133-139 0924-090X 66:1-2<133 2011 66 11071 https://doi.org/10.1007/s11071-010-9915-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9915-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Danca Marius-F Dept. of Mathematics and Computer Science, Avram Iancu University, 400380, Cluj-Napoca, Romania aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 66/1-2(2011-10-01), 133-139 0924-090X 66:1-2<133 2011 66 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer