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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Bibliographic Details
Published in:Complexity (New York, N.Y.) N.Y.), 2020, Vol.2020 (2020), p.1-13
Main Authors: Qu, Haidong, Liu, Xuan, She, Zihang
Format: Article
Language:English
Subjects:
Acoustic waves
Acoustics
Analysis
Boundary conditions
Computer graphics
Control theory
Derivatives
Differential equations
Exact solutions
Graphics software
Integrals
Mathematical models
Methods
Partial differential equations
Researchers
Two dimensional models
Wave equations
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Summary: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.
ISSN:1076-2787
1099-0526
DOI:10.1155/2020/7232907