Approximate solutions to fractional differential equations

doi:10.1007/s10483-023-3041-9

Applied Mathematics and Mechanics (English Edition) ›› 2023, Vol. 44 ›› Issue (10): 1791-1802.doi: https://doi.org/10.1007/s10483-023-3041-9

Approximate solutions to fractional differential equations

Yue LIU^1,2,3, Zhen ZHAO⁴, Yanni ZHANG⁵, Jing PANG^1,3

1. College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China;
2. Department of Mathematics and Computer Science, Hetao College, Bayannur 015000, Inner Mongolia Autonomous Region, China;
3. Inner Mongolia Key Laboratory of Statistical Analysis Theory for Life Data and Neural Network Modeling, Hohhot 010051, China;
4. College of Mathematics and Statistics, Ningbo University, Ningbo 315211, Zhejiang Province, China;
5. College of Science, Liaoning University of Technology, Jinzhou 121001, Liaoning Province, China

收稿日期:2023-06-13 修回日期:2023-08-24 发布日期:2023-09-25
通讯作者: Jing PANG, E-mail: pang_j@imut.edu.cn
基金资助:
the National Natural Science Foundation of China (No.10561151), the Basic Science Research Fund in the Universities Directly Under the Inner Mongolia Autonomous Region (No.JY20220003), and the Scientific Research Project of Hetao College of China (No.HYZQ202122)

Approximate solutions to fractional differential equations

Yue LIU^1,2,3, Zhen ZHAO⁴, Yanni ZHANG⁵, Jing PANG^1,3

1. College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China;
2. Department of Mathematics and Computer Science, Hetao College, Bayannur 015000, Inner Mongolia Autonomous Region, China;
3. Inner Mongolia Key Laboratory of Statistical Analysis Theory for Life Data and Neural Network Modeling, Hohhot 010051, China;
4. College of Mathematics and Statistics, Ningbo University, Ningbo 315211, Zhejiang Province, China;
5. College of Science, Liaoning University of Technology, Jinzhou 121001, Liaoning Province, China

Received:2023-06-13 Revised:2023-08-24 Published:2023-09-25
Contact: Jing PANG, E-mail: pang_j@imut.edu.cn
Supported by:
the National Natural Science Foundation of China (No.10561151), the Basic Science Research Fund in the Universities Directly Under the Inner Mongolia Autonomous Region (No.JY20220003), and the Scientific Research Project of Hetao College of China (No.HYZQ202122)

摘要/Abstract

摘要： In this paper, the time-fractional coupled viscous Burgers' equation (CVBE) and Drinfeld-Sokolov-Wilson equation (DSWE) are solved by the Sawi transform coupled homotopy perturbation method (HPM). The approximate series solutions to these two equations are obtained. Meanwhile, the absolute error between the approximate solution given in this paper and the exact solution given in the literature is analyzed. By comparison of the graphs of the function when the fractional order $\alpha$ takes different values, the properties of the equations are given as a conclusion.

关键词: Caputo fractional derivative, coupled viscous Burgers' equation (CVBE), Drinfeld-Sokolov-Wilson equation (DSWE), Sawi transform, homotopy perturbation method (HPM)

Abstract: In this paper, the time-fractional coupled viscous Burgers' equation (CVBE) and Drinfeld-Sokolov-Wilson equation (DSWE) are solved by the Sawi transform coupled homotopy perturbation method (HPM). The approximate series solutions to these two equations are obtained. Meanwhile, the absolute error between the approximate solution given in this paper and the exact solution given in the literature is analyzed. By comparison of the graphs of the function when the fractional order $\alpha$ takes different values, the properties of the equations are given as a conclusion.

Key words: Caputo fractional derivative, coupled viscous Burgers' equation (CVBE), Drinfeld-Sokolov-Wilson equation (DSWE), Sawi transform, homotopy perturbation method (HPM)

中图分类号:

76B15
35R11

Yue LIU, Zhen ZHAO, Yanni ZHANG, Jing PANG. Approximate solutions to fractional differential equations[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(10): 1791-1802.

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Approximate solutions to fractional differential equations

Approximate solutions to fractional differential equations

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