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[1]陈景华*,陈雪娟,章红梅.基于广义Oldroyd-B流体问题的高维多项时间分数阶偏微分方程的解析解[J].厦门大学学报(自然科学版),2019,58(03):397-401.[doi:10.6043/j.issn.0438-0479.201806026]
 CHEN Jinghua*,CHEN Xuejuan,ZHANG Hongmei.Analytical solutions of multi-term fractional differential equations in high dimensions and application to generalized Oldroyd-B fluid[J].Journal of Xiamen University(Natural Science),2019,58(03):397-401.[doi:10.6043/j.issn.0438-0479.201806026]
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基于广义Oldroyd-B流体问题的高维多项时间分数阶偏微分方程的解析解(PDF/HTML)
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《厦门大学学报(自然科学版)》[ISSN:0438-0479/CN:35-1070/N]

卷:
58卷
期数:
2019年03期
页码:
397-401
栏目:
研究论文
出版日期:
2019-05-28

文章信息/Info

Title:
Analytical solutions of multi-term fractional differential equations in high dimensions and application to generalized Oldroyd-B fluid
文章编号:
0438-0479(2019)03-0397-05
作者:
陈景华1*陈雪娟1章红梅2
1.集美大学理学院,福建 厦门 361021; 2.福州大学数学与计算机科学学院,福建 福州 350108
Author(s):
CHEN Jinghua1*CHEN Xuejuan1ZHANG Hongmei2
1.School of Sciences,Jimei University,Xiamen 361021,China; 2.School of Mathematical and Computer Sciences,Fuzhou University,Fuzhou 350108,China
关键词:
多项时间分数阶偏微分方程 分离变量法 广义Oldroyd-B流体 多重Mittag-Leffler函数
Keywords:
multi-term time fractional differential equation separating variables method generalized Oldroyd-B fluid multivariate Mittag-Leffler functions
分类号:
O 241.82
DOI:
10.6043/j.issn.0438-0479.201806026
文献标志码:
A
摘要:
提出两类高维多项时间分数阶偏微分方程的模型,此模型可用来描述广义黏弹性Oldroyd-B流体的剪应力和剪切速率之间的非线性关系.采用分离变量法将此分数阶偏微分方程转化成分数阶常微分方程,从而得到此高维多项时间分数阶偏微分方程的解析解,解的形式以多重Mittag-Leffler函数的形式给出.
Abstract:
This paper presents two types of multi-term fractional differential equations in high dimensions.These models can be used to describe the nonlinear relationship between the shear stress and the shear rate of generalized viscoelastic Oldroyd-B fluid.These equations are transformed into fractional-order ordinary differential counterparts.Analytical solutions are expressed in multivariate Mittag-Leffler functions.

参考文献/References:

[1] PODLUBNY I.Fractional differential equations:an introduction to fractional derivatives,fractional differential equations,to methods of their solution and some of their applications[M].New York:Academic Press,1999:296-298.
[2] SONG D Y,JIANG T Q.Study on the constitutive equation with fractional derivative for the viscoelastic fluids-modified Jeffreys model and its application[J].Rheol Acta,1998,37:512-517.
[3] HILFER R.Applications of fractional calculus in physics[C].Singapore:World Scientific Press,2000:116-120.
[4] FETECAU C,FETECAU C,KHAN M,et al.Decay of a potential vortex in a generalized Oldroyd-B fluid[J].Appl Math Comput,2008,205:497-506.
[5] KHAN M.The Rayleigh-Stokes problem for an edge in a viscoelastic fluid with a fractional derivative model[J].Non Linear Anal RWA,2009,10:3190-3195.
[6] NADEEM S.General periodic flows of fractional Oldroyd-B fluid for an edge[J].Phys Lett A,2007,368:181-187.
[7] KHAN M,HAYAT T,ASGHAR S.Exact solution for MHD flow of a generalized Oldroyd-B fluid with modified Darcy’s law[J].Int J Eng Sci,2006,44:333-339.
[8] QI H T,XU M Y.Some unsteady unidirectional flows of a generalized Oldroyd-B fluid with fractional derivative[J].Appl Math Comput,2009,33:4184-4191.
[9] ZHENG L C,LIU Y Q,ZHANG X X.Exact solution for MHD flow of generalized Oldroyd-B fluid due to an infinite accelerating plate[J].Mathematical and Computer Modelling, 2011,54:780-788.
[10] LUCHKO Y,GORENFLO R.An operational method for solving fractional differential equations with the Caputo derivatives[J].Acta Math Vietnam,1999,24:207-233.
[11] 王学彬,刘发旺.二维和三维的时间分数阶电报方程的解析解[J].山东大学学报(理学版),2012,47(8):114-121.[1] PODLUBNY I.Fractional differential equations:an introduction to fractional derivatives,fractional differential equations,to methods of their solution and some of their applications[M].New York:Academic Press,1999:296-298.
[2] SONG D Y,JIANG T Q.Study on the constitutive equation with fractional derivative for the viscoelastic fluids-modified Jeffreys model and its application[J].Rheol Acta,1998,37:512-517.
[3] HILFER R.Applications of fractional calculus in physics[C].Singapore:World Scientific Press,2000:116-120.
[4] FETECAU C,FETECAU C,KHAN M,et al.Decay of a potential vortex in a generalized Oldroyd-B fluid[J].Appl Math Comput,2008,205:497-506.
[5] KHAN M.The Rayleigh-Stokes problem for an edge in a viscoelastic fluid with a fractional derivative model[J].Non Linear Anal RWA,2009,10:3190-3195.
[6] NADEEM S.General periodic flows of fractional Oldroyd-B fluid for an edge[J].Phys Lett A,2007,368:181-187.
[7] KHAN M,HAYAT T,ASGHAR S.Exact solution for MHD flow of a generalized Oldroyd-B fluid with modified Darcy’s law[J].Int J Eng Sci,2006,44:333-339.
[8] QI H T,XU M Y.Some unsteady unidirectional flows of a generalized Oldroyd-B fluid with fractional derivative[J].Appl Math Comput,2009,33:4184-4191.
[9] ZHENG L C,LIU Y Q,ZHANG X X.Exact solution for MHD flow of generalized Oldroyd-B fluid due to an infinite accelerating plate[J].Mathematical and Computer Modelling, 2011,54:780-788.
[10] LUCHKO Y,GORENFLO R.An operational method for solving fractional differential equations with the Caputo derivatives[J].Acta Math Vietnam,1999,24:207-233.
[11] 王学彬,刘发旺.二维和三维的时间分数阶电报方程的解析解[J].山东大学学报(理学版),2012,47(8):114-121.

备注/Memo

备注/Memo:
收稿日期:2018-06-21 录用日期:2018-11-06
基金项目:福建省自然科学基金(2017J01557,2017J01555); 福建省教育厅科技项目(JAT160274,JT180262); 集美大学校基金(ZC2016022)
*通信作者:cjhdzdz@163.com
更新日期/Last Update: 1900-01-01