文献类型：期刊文献

英文题名：New approximations for solving the Caputo-type fractional partial differential equations

作者：Ren, Jincheng[1];Sun, Zhi-zhong[2];Dai, Weizhong[3,4]

通讯作者：Dai, WZ[1]

机构：[1]Henan Univ Econ & Law, Coll Math & Informat Sci, Zhengzhou, Peoples R China;[2]Southeast Univ, Dept Math, Nanjing, Jiangsu, Peoples R China;[3]Louisiana Tech Univ, Math & Stat, Ruston, LA 71272 USA;[4]Minnan Normal Univ, Coll Math & Stat, Zhangzhou, Peoples R China

第一机构：河南财经政法大学数学与信息科学学院

通讯机构：[1]corresponding author), Louisiana Tech Univ, Math & Stat, Ruston, LA 71272 USA.

年份：2016

卷号：40

期号：4

起止页码：2625-2636

外文期刊名：APPLIED MATHEMATICAL MODELLING

收录：;EI(收录号：20160601906247);Scopus(收录号：2-s2.0-84956898226);WOS:【SCI-EXPANDED(收录号:WOS:000370767000012)】；

基金：The financial supports from the Major Research Plan of Henan University of Economics and Law in 2014 and Foundation of Henan Educational Committee (No. 15A110009) for the first author, National Natural Science Foundation of China (no. 11271068) for the first and second authors and the National Science Foundation (NSF EPS-1003897) for the third author are gratefully acknowledged.

语种：英文

外文关键词：Fractional partial differential equation; Caputo-type derivative; Finite difference scheme; Laplace transform

摘要：Partial differential equations with the Caputo-type fractional derivative have been used in many engineering applications. Because the Caputo-type fractional derivative is an integral of the solution with respect to time, the numerical scheme for solving this type of fractional differential equations requires using the values of all previous time steps. This needs a large size of memory to store the necessary data when computing, which may lead to a memory problem in computer, particularly when solving systems of multi-dimensional fractional differential equations. For this purpose, this article presents a new approximation for solving the fractional differential equations using the Laplace transform method. The obtained differential equations will then be solved using some conventional two or three-level in time finite difference schemes, which reduce the computational cost significantly. For simplicity, the method is presented in 1D and is illustrated by several 1D and 2D examples. In practical, this method can be readily used for solving more complex cases within a reasonable accuracy. (C) 2015 Elsevier Inc. All rights reserved.