Homotopy Analysis Method for Three Types of Fractional Partial Differential Equations
In this paper, three types of fractional order partial differential equations, including the fractional Cauchy–Riemann equation, fractional acoustic wave equation, and two-dimensional space partial differential equation with time-fractional-order, are considered, and these models are obtained from t...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/7232907 |
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| _version_ | 1849396578402435072 |
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| author | Haidong Qu Zihang She Xuan Liu |
| author_facet | Haidong Qu Zihang She Xuan Liu |
| author_sort | Haidong Qu |
| collection | DOAJ |
| description | In this paper, three types of fractional order partial differential equations, including the fractional Cauchy–Riemann equation, fractional acoustic wave equation, and two-dimensional space partial differential equation with time-fractional-order, are considered, and these models are obtained from the standard equations by replacing an integer-order derivative with a fractional-order derivative in Caputo sense. Firstly, we discuss the fractional integral and differential properties of several functions which are derived from the Mittag-Leffler function. Secondly, by using the homotopy analysis method, the exact solutions for fractional order models mentioned above with suitable initial boundary conditions are obtained. Finally, we draw the computer graphics of the exact solutions, the approximate solutions (truncation of finite terms), and absolute errors in the limited area, which show that the effectiveness of the homotopy analysis method for solving fractional order partial differential equations. |
| format | Article |
| id | doaj-art-afdec24dcea044268c37bd71f9bf88d9 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-afdec24dcea044268c37bd71f9bf88d92025-08-20T03:39:18ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/72329077232907Homotopy Analysis Method for Three Types of Fractional Partial Differential EquationsHaidong Qu0Zihang She1Xuan Liu2Department of Mathematics, Hanshan Normal University, Chaozhou 515041, ChinaDepartment of Mathematics, Hanshan Normal University, Chaozhou 515041, ChinaDepartment of Mathematics, Hanshan Normal University, Chaozhou 515041, ChinaIn this paper, three types of fractional order partial differential equations, including the fractional Cauchy–Riemann equation, fractional acoustic wave equation, and two-dimensional space partial differential equation with time-fractional-order, are considered, and these models are obtained from the standard equations by replacing an integer-order derivative with a fractional-order derivative in Caputo sense. Firstly, we discuss the fractional integral and differential properties of several functions which are derived from the Mittag-Leffler function. Secondly, by using the homotopy analysis method, the exact solutions for fractional order models mentioned above with suitable initial boundary conditions are obtained. Finally, we draw the computer graphics of the exact solutions, the approximate solutions (truncation of finite terms), and absolute errors in the limited area, which show that the effectiveness of the homotopy analysis method for solving fractional order partial differential equations.http://dx.doi.org/10.1155/2020/7232907 |
| spellingShingle | Haidong Qu Zihang She Xuan Liu Homotopy Analysis Method for Three Types of Fractional Partial Differential Equations Complexity |
| title | Homotopy Analysis Method for Three Types of Fractional Partial Differential Equations |
| title_full | Homotopy Analysis Method for Three Types of Fractional Partial Differential Equations |
| title_fullStr | Homotopy Analysis Method for Three Types of Fractional Partial Differential Equations |
| title_full_unstemmed | Homotopy Analysis Method for Three Types of Fractional Partial Differential Equations |
| title_short | Homotopy Analysis Method for Three Types of Fractional Partial Differential Equations |
| title_sort | homotopy analysis method for three types of fractional partial differential equations |
| url | http://dx.doi.org/10.1155/2020/7232907 |
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