Maximum principle and numerical method for the multi-term time-space Riesz-Caputo fractional differential equations

被引：68
|
作者：
Ye, H. [1 ]
Liu, F. [2 ]
Anh, V. [2 ]
Turner, I. [2 ]
机构：
[1] Donghua Univ, Dept Appl Math, Shanghai 201620, Peoples R China
[2] Queensland Univ Technol, Brisbane, Qld 4001, Australia
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 227卷
关键词：
Multi-term time-space fractional; differential equation; Riesz-Caputo fractional derivative; Maximum principle; Predictor-corrector method; L1/L2-approximation method; ADVECTION-DISPERSION EQUATION; BOUNDARY-VALUE PROBLEMS; DIFFUSION EQUATION;
D O I：
10.1016/j.amc.2013.11.015
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The maximum principle for the space and time-space fractional partial differential equations is still an open problem. In this paper, we consider a multi-term time-space Riesz-Caputo fractional differential equations over an open bounded domain. A maximum principle for the equation is proved. The uniqueness and continuous dependence of the solution are derived. Using a fractional predictor-corrector method combining the L1 and L2 discrete schemes, we present a numerical method for the specified equation. Two examples are given to illustrate the obtained results. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码：531 / 540
页数：10
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