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2010 Stability and Convergence of an Effective Numerical Method for the Time-Space Fractional Fokker-Planck Equation with a Nonlinear Source Term
Qianqian Yang, Fawang Liu, Ian Turner
Int. J. Differ. Equ. 2010(SI1): 1-22 (2010). DOI: 10.1155/2010/464321

Abstract

Fractional Fokker-Planck equations (FFPEs) have gained much interest recently for describing transport dynamics in complex systems that are governed by anomalous diffusion and nonexponential relaxation patterns. However, effective numerical methods and analytic techniques for the FFPE are still in their embryonic state. In this paper, we consider a class of time-space fractional Fokker-Planck equations with a nonlinear source term (TSFFPENST), which involve the Caputo time fractional derivative (CTFD) of order α (0, 1) and the symmetric Riesz space fractional derivative (RSFD) of order μ (1, 2]. Approximating the CTFD and RSFD using the L1-algorithm and shifted Grünwald method, respectively, a computationally effective numerical method is presented to solve the TSFFPE-NST. The stability and convergence of the proposed numerical method are investigated. Finally, numerical experiments are carried out to support the theoretical claims.

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Qianqian Yang. Fawang Liu. Ian Turner. "Stability and Convergence of an Effective Numerical Method for the Time-Space Fractional Fokker-Planck Equation with a Nonlinear Source Term." Int. J. Differ. Equ. 2010 (SI1) 1 - 22, 2010. https://doi.org/10.1155/2010/464321

Information

Received: 25 May 2009; Revised: 20 August 2009; Accepted: 28 September 2009; Published: 2010
First available in Project Euclid: 26 January 2017

zbMATH: 1203.82068
MathSciNet: MR2575294
Digital Object Identifier: 10.1155/2010/464321

Rights: Copyright © 2010 Hindawi

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