The Numerical Solutions of a Two-Dimensional Space-Time Riesz-Caputo Fractional Diffusion Equation

An International Journal of Optimization and Control: Theories & Applications

article

Necati OZDEMIR¹  Derya AVCI¹  Beyza Billur ISKENDER¹ 

[1] Department of Mathematics, Faculty of Science and Arts,Balıkesir University

关键词: Caputo;    Riesz;    Gr¨unwald-Letnikov;    Fourier Series;    Laplace Transform;   

DOI  :  10.11121/ijocta.01.2011.0028

学科分类：地球科学(综合)

来源: Balikesir University

【 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.

【 授权许可】

CC BY