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Psi-Series Approach to Fractional Equations

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Fractional Dynamics

Part of the book series: Nonlinear Physical Science ((NPS,volume 0))

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Abstract

Psi-series approach to the question of integrability is not concerned with the display of explicit functions. In this approach the existence of Laurent series for each dependent variables is considered. In general, the series may not be summable to an explicit form, but does represent an analytic function. The essential feature of this Laurent series is that it is an expansion about a particular type of movable singularity, i.e., a pole. The existence of these Laurent series is intimately connected with the singularity analysis of differential equations (Ince, 1927). Beginning with the pioneering contributions by Painleve (Painleve, 1973), studies of these properties of nonlinear differential equations become an active field of research (Bureau, 1964; Cosgrove and Scoufis, 1993; Tabor, 1989; Roy-Chowdhury, 2000).

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Tarasov, V.E. (2010). Psi-Series Approach to Fractional Equations. In: Fractional Dynamics. Nonlinear Physical Science, vol 0. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14003-7_10

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