A HIGH ORDER SCHEME FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH THE CAPUTO-HADAMARD DERIVATIVE  

作　　者：Xingyang Ye Junying Cao Chuanju Xu 

机构地区：[1]School of Science,Jimei University,Xiamen 361021,China [2]School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China [3]School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing,Xiamen University,Xiamen 361005,China

出　　处：《Journal of Computational Mathematics》2025年第3期615-640,共26页计算数学(英文)

基　　金：supported by the Fujian Alliance of Mathematics(Grant No.2024SXLMMS03);by the Natural Science Foundation of Fujian Province of China(Grant No.2022J01338);supported by the NSFC(Grant Nos.12361083,62341115);by the Foundation of Guizhou Science and Technology Department(Grant No.QHKJC-ZK[2024]YB497);by the Natural Science Research Project of Department of Education of Guizhou Province(Grant No.QJJ2023012);by the Science Research Fund Support Project of the Guizhou Minzu University(Grant No.GZMUZK[2023]CXTD05);supported by the NSFC(Grant No.12371408).

摘　　要：In this paper,we consider numerical solutions of the fractional diffusion equation with theαorder time fractional derivative defined in the Caputo-Hadamard sense.A high order time-stepping scheme is constructed,analyzed,and numerically validated.The contribution of the paper is twofold:1)regularity of the solution to the underlying equation is investigated,2)a rigorous stability and convergence analysis for the proposed scheme is performed,which shows that the proposed scheme is 3+αorder accurate.Several numerical examples are provided to verify the theoretical statement.

关 键 词：Caputo-Hadamard derivative Fractional differential equations High order scheme Stability and convergence analysis 

分 类 号：O241.3[理学—计算数学]