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A new analytic solution for fractional chaotic dynamical systems using the differential transform method. (English) Zbl 1221.65191
Summary: Nonlinear differential equations with fractional derivatives give general representations of real life phenomena. In this paper, a modification of the differential transform method (DTM) for solving the nonlinear fractional differential equation is introduced for the first time. The new algorithm is simple and gives an accurate solution. Moreover the new solution is continuous and analytic on each subinterval. A fractional Chen system is considered, to demonstrate the efficiency of the algorithm. The results obtained show good agreement with the generalized Adams-Bashforth-Moulton method.

MSC:
65L99 Numerical methods for ordinary differential equations
34A08 Fractional ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
45J05 Integro-ordinary differential equations
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