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：Bo Yu Xiaoyun Jiang Haitao Qi 

作者机构：School of MathematicsShandong University School of Mathematics and StatisticsShandong University 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2015年第31卷第2期

页      面：153-161页

核心收录：

学科分类：080704[工学-流体机械及工程] 07[理学] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 070102[理学-计算数学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation of China(Grants 11472161,11102102,and 91130017) the Independent Innovation Foundation of Shandong University(Grant 2013ZRYQ002) the Natural Science Foundation of Shandong Province(Grant ZR2014AQ015) 

主　　题：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 *** implicit numerical method is employed to solve the direct *** 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 *** order to demonstrate the effectiveness of the proposed numerical method,two cases in which the measurement values contain random measurement error or not are *** computational results demonstrate that the proposed numerical method could efficiently obtain the optimal estimation of the unknown order of a RiemannLiouville fractional derivative for a fractional Stokes＇ first problem for a heated generalized second grade fluid.