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

(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)

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

Analytical solutions of multi-term fractional differential equations in high dimensions and application to generalized Oldroyd-B fluid
CHEN Jinghua1*,CHEN Xuejuan1,ZHANG Hongmei2

(1.School of Sciences,Jimei University,Xiamen 361021,China; 2.School of Mathematical and Computer Sciences,Fuzhou University,Fuzhou 350108,China)

multi-term time fractional differential equation; separating variables method; generalized Oldroyd-B fluid; multivariate Mittag-Leffler unctions

DOI: 10.6043/j.issn.0438-0479.201806026

备注

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.

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.