期刊名称：International Journal of Differential Equations
印刷版ISSN：1687-9643
电子版ISSN：1687-9651
出版年度：2010
卷号：2010
DOI：10.1155/2010/464321
出版社：Hindawi Publishing Corporation
摘要：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.
