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浙江大学学报（理学版）
浙江大学学报（理学版）  2016, Vol. 43 Issue (4): 406-410    DOI: 10.3785/j.issn.1008-9497.2016.04.005
数学与计算机科学     
混合边界条件下广义二维多项时间分数阶扩散方程的解析解
王学彬
武夷学院 数学与计算机学院, 福建 武夷山 354300
Analytical solution of the generalized muti-term time-fractional diffusion equation in two-dimensions with mixed boundary condition
WANG Xuebin
School of Mathematics and Computer, Wuyi University, Wuyishan 354300, Fujian Province, China
 全文: PDF(519 KB)  
摘要： 广义多项时间分数阶扩散方程已被用于描述一些重要的物理现象，目前，有关该类方程在高维情形下满足混合边界条件的研究仍较少.利用分离变量法考虑有界区域上广义二维多项时间分数阶扩散方程，方程中关于时间变量的分数阶导数采用Caputo分数阶导数的定义，其阶分别定义在［0，1］，［1，2］.而关于空间变量的偏导数则定义为传统的整数阶导数（二阶），得到了有界区域上广义二维多项时间分数阶扩散方程满足非齐次混合边界条件的解析解.亦可用于求解其他类型的满足不同边界条件的分数阶微分方程的解析解.
关键词： 混合边界条件;  分离变量法;  分数阶扩散方程    
Abstract: Generalized multi-term time-fractional diffusion equations have been used to describe important physical phenomena. However, studies on multi-term time-fractional diffusion equations with mixed boundary conditions in high dimensional conditions are still limited. In this paper,a method of separating variables was effectively implemented to solve a generalized multi-term time-fractional diffusion equation (GMTDE) in a finite domain.In this equation, the multi-term time-fractional derivatives were defined in the Caputo sense, whose orders belonged to the intervals [0,1], [1,2], respectively. The space partial derivatives were classical integer order derivatives whose order were 2. We discussed and derived the analytical solution of the GMTDE in two dimensions meeting nonhomogeneous mixed boundary conditions.The technique reported can be applied to other kinds of fractional differential equations with different boundary conditions.
Key words: mixed boundary conditions    method of separating variables    time-fractional diffusion equation
收稿日期: 2015-03-26 出版日期: 2016-04-28
CLC:  O241.82  
基金资助: 福建省自然科学基金资助项目（2016J01682）；福建省本科高校教育教学改革研究项目（JAS151344）；武夷学院青年教师专项科研基金（xq201022）；武夷学院质量工程项目（Jgzk201019）.
作者简介: 王学彬(1976-),ORCID:http://orcid.org/0000-0002-1066-3524,男,硕士,副教授,主要从事分数阶微积分研究,E-mail:wxbnp@163.com.
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王学彬

引用本文:

王学彬. 混合边界条件下广义二维多项时间分数阶扩散方程的解析解[J]. 浙江大学学报（理学版）, 2016, 43(4): 406-410.

WANG Xuebin. Analytical solution of the generalized muti-term time-fractional diffusion equation in two-dimensions with mixed boundary condition. Journal of ZheJIang University(Science Edition), 2016, 43(4): 406-410.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2016.04.005    或    https://www.zjujournals.com/sci/CN/Y2016/V43/I4/406

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