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Research Papers

A New Numerical Method for Solving Nonlinear Fractional Fokker–Planck Differential Equations

[+] Author and Article Information
BeiBei Guo

Department of Mathematics,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: guobei066@126.com

Wei Jiang

Department of Mathematics,
Harbin Institute of Technology at Weihai,
Shandong 264209, China
e-mail: jiangwei015@163.com

ChiPing Zhang

Department of Mathematics,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: zcp@hit.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 17, 2016; final manuscript received January 21, 2017; published online March 9, 2017. Assoc. Editor: Anindya Chatterjee.

J. Comput. Nonlinear Dynam 12(5), 051004 (Mar 09, 2017) (6 pages) Paper No: CND-16-1434; doi: 10.1115/1.4035896 History: Received September 17, 2016; Revised January 21, 2017

The nonlinear fractional-order Fokker–Planck differential equations have been used in many physical transport problems which take place under the influence of an external force filed. Therefore, high-accuracy numerical solutions are always needed. In this article, reproducing kernel theory is used to solve a class of nonlinear fractional Fokker–Planck differential equations. The main characteristic of this approach is that it induces a simple algorithm to get the approximate solution of the equation. At the same time, an effective method for obtaining the approximate solution is established. In addition, some numerical examples are given to demonstrate that our method has lesser computational work and higher precision.

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Figures

Grahic Jump Location
Fig. 1

The comparison of exact solution and approximation solution of Example 1

Grahic Jump Location
Fig. 2

The three-dimensional exact solution of Example 2

Grahic Jump Location
Fig. 3

The three-dimensional approximate solution of Example2

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