Homotopy Analysis Method for Three Types of Fractional Partial Differential Equations
Joint Authors
Qu, Haidong
Liu, Xuan
She, Zihang
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-07-10
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Qu, Haidong& She, Zihang& Liu, Xuan. 2020. Homotopy Analysis Method for Three Types of Fractional Partial Differential Equations. Complexity،Vol. 2020, no. 2020, pp.1-13.
https://search.emarefa.net/detail/BIM-1143644
Modern Language Association (MLA)
Qu, Haidong…[et al.]. Homotopy Analysis Method for Three Types of Fractional Partial Differential Equations. Complexity No. 2020 (2020), pp.1-13.
https://search.emarefa.net/detail/BIM-1143644
American Medical Association (AMA)
Qu, Haidong& She, Zihang& Liu, Xuan. Homotopy Analysis Method for Three Types of Fractional Partial Differential Equations. Complexity. 2020. Vol. 2020, no. 2020, pp.1-13.
https://search.emarefa.net/detail/BIM-1143644
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1143644