文章基本信息

标题：The Numerical Solutions of a Two-Dimensional Space-Time Riesz-Caputo Fractional Diffusion Equation
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作者：Necati OZDEMIR ; Derya AVCI ; Beyza Billur ISKENDER 等
期刊名称：An International Journal of Optimization and Control: Theories & Applications (IJOCTA)
印刷版ISSN：2146-5703
出版年度：2011
卷号：1
期号：1
页码：17-26
DOI：10.11121/ijocta.01.2011.0028
语种：English
出版社：An International Journal of Optimization and Control: Theories & Applications (IJOCTA)
摘要：This paper is concerned with the numerical solutions of a two dimensional space-time fractional differential equation used to model the dynamic properties of complex systems governed by anomalous diffusion. The space-time fractional anomalous diffusion equation is defined by replacing second order space and first order time derivatives with Riesz and Caputo operators, respectively. By using Laplace and Fourier transforms, a general representation of analytical solution is obtained as Mittag-Leffler function. Gr\"{u}nwald-Letnikov (GL) approximation is also used to find numerical solution of the problem. Finally, simulation results for two examples illustrate the comparison of the analytical and numerical solutions and also validity of the GL approach to this problem.
关键词：Caputo, Riesz, GrÂ¨unwald-Letnikov, Fourier Series, Laplace Transform