A search for a spectral technique to solve nonlinear fractional\n differential equations

2015/08/13 by Malgorzata Turalska, Turalska, Malgorzata, Bruce J. West +1
Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1508.03222

Abstract

A spectral decomposition method is used to obtain solutions to a class of\nnonlinear differential equations. We extend this approach to the analysis of\nthe fractional form of these equations and demonstrate the method by applying\nit to the fractional Riccati equation, the fractional logistic equation and a\nfractional cubic equation. The solutions reduce to those of the ordinary\nnonlinear differential equations, when the order of the fractional derivative\nis \α =1. The exact analytic solutions to the fractional nonlinear\ndifferential equations are not known, so we evaluate how well the derived\nsolutions satisfy the corresponding fractional dynamic equations. In the three\ncases we find a small, apparently generic, systematic error that we are not\nable to fully interpret.\n

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