标题:An inverse problem to estimate an unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes' first problem for a heated generalized second grade fluid
作者:Yu, Bo; Jiang, Xiaoyun; Qi, Haitao
作者机构:[Yu Bo] School of Mathematics, Shandong University, Ji'nan, Shandong 250100, China.;[Jiang Xiaoyun] School of Mathematics, Shandong University, Jin'an 更多
通讯作者:Jiang, Xiaoyun(wqjxyf@sdu.edu.cn)
通讯作者地址:[Jiang, XY]Shandong Univ, Sch Math, Jinan 250100, Peoples R China.
来源:力学学报
出版年:2015
卷:31
期:2
页码:153-161
DOI:10.1007/s10409-015-0408-7
关键词:Riemann-Liouville fractional derivative; Generalized second grade fluid;; Inverse problem; Implicit numerical method; Fractional sensitivity; equation
摘要:In this paper, we propose a numerical method to estimate the unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes' first problem for a heated generalized second grade fluid. The implicit numerical method is employed to solve the direct problem. For the inverse problem, we first obtain the fractional sensitivity equation by means of the digamma function, and then we propose an efficient numerical method, that is, the Levenberg-Marquardt algorithm based on a fractional derivative, to estimate the unknown order of a Riemann-Liouville fractional derivative. In order to demonstrate the effectiveness of the proposed numerical method, two cases in which the measurement values contain random measurement error or not are considered. The computational results demonstrate that the proposed numerical method could efficiently obtain the optimal estimation of the unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes' first problem for a heated generalized second grade fluid.; In this paper, we propose a numerical method to estimate the unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes first problem for a heated generalized second grade fluid. The implicit numerical method is employed to solve the direct problem. For the inverse problem, we obtain the fractional sensitivity equation by means of the digamma function. Numerical simulations demonstrate the effectiveness of the proposed method.
收录类别:EI;CSCD;SCOPUS;SCIE
WOS核心被引频次:16
Scopus被引频次:17
资源类型:期刊论文
原文链接:https://www.scopus.com/inward/record.uri?eid=2-s2.0-84929962305&doi=10.1007%2fs10409-015-0408-7&partnerID=40&md5=7c6bcab1060abfb81569f44146362846
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