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  

Analytical solutions of multi-term fractional differential equations in high dimensions and application to generalized Oldroyd-B fluid

作　　者：陈景华[1] 陈雪娟[1] 章红梅[2] CHEN Jinghua;CHEN Xuejuan;ZHANG Hongmei(School of Sciences,Jimei University,Xiamen 361021,China;School of Mathematical and Computer Sciences,Fuzhou University,Fuzhou 350108,China)

机构地区：[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

出　　处：《厦门大学学报（自然科学版）》2019年第3期397-401,共5页Journal of Xiamen University：Natural Science

基　　金：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)

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.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.

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 

分 类 号：O241.82[理学—计算数学]