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2013 | 11 | 10 | 1178-1193
Article title

Numerical solutions and analysis of diffusion for new generalized fractional advection-diffusion equations

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EN
Abstracts
EN
In this paper we study a class of new Generalized Fractional Advection-Diffusion Equations (GFADEs) with a new Generalized Fractional Derivative (GFD) proposed last year. The new GFD is defined in the Caputo sense using a weight function and a scale function. The GFADE is discussed in a bounded domain, and numerical solutions for two examples consisting of a linear and a nonlinear GFADE are obtained using an implicit finite difference approach. The stability of the numerical scheme is investigated, and the order of convergence is estimated numerically. Numerical results illustrate that the finite difference scheme is simple and effective for solving the GFADEs. We investigate the influence of weight and scale functions on the diffusion of GFADEs. Linear and nonlinear stretching and contracting functions are considered. It is found that an increasing weight function increases the rate of diffusion, and a scale function can stretch or contract the diffusion on the time domain.
Publisher

Journal
Year
Volume
11
Issue
10
Pages
1178-1193
Physical description
Dates
published
1 - 10 - 2013
online
19 - 12 - 2013
Contributors
author
  • Department of Applied Mathematics, School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, People’s Republic of China, xuyufeng@csu.edu.cn
author
  • Mechanical Engineering and Energy Processes, Southern Illinois University, Carbondale, Illinois, 62901, USA, om@engr.siu.edu
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Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0295-0
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