Solutions to Class of Linear and Nonlinear Fractional Differential Equations

In this paper, the fractional auxiliary sub-equation expansion method is proposed to solve nonlinear fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional KdV equation, the space-time fractional RLW equation, the space-time fractional...

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Bibliographic Details
Published in:Communications in theoretical physics 2016-02, Vol.65 (2), p.127-135
Main Authors: Abdel-Salam, Emad A-B., Hassan, Gamal F.
Format: Article
Language:English
Subjects:
Boussinesq equations
Constants
Differential equations
exact solutions
fractional auxiliary sub-equation expansion method
linear and nonlinear fractional differential equation
Mathematical analysis
Mittag-Leffler function method
modified Riemann-Liouville derivatives
Nonlinearity
Theoretical physics
Trigonometric functions
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Summary:In this paper, the fractional auxiliary sub-equation expansion method is proposed to solve nonlinear fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional KdV equation, the space-time fractional RLW equation, the space-time fractional Boussinesq equation, and the (3+1)-space-time fractional ZK equation. The solutions are expressed in terms of fractional hyperbolic and fractional trigonometric functions. These solutions are useful to understand the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The analytical solution of homogenous linear FDEs with constant coefficients are obtained by using the series and the Mittag-Leffler function methods. The obtained results recover the well-know solutions when α = 1.
ISSN:0253-6102
1572-9494
DOI:10.1088/0253-6102/65/2/127