Solutions to Class of Linear and Nonlinear Fractional Differential Equations |
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Authors: | Emad A-B Abdel-Salam Gamal F Hassan |
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Institution: | 1.Department of Mathematics, Faculty of Science, Assiut University, New Valley Branch, El-Kharja 72511, Egypt;2.Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt;3.Department of Mathematics, Faculty of Science, Northern Border University, Arar 91431, Saudi Arabia |
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Abstract: | 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. |
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Keywords: | linear and nonlinear fractional differential equation modified Riemann-Liouville derivatives exact solutions fractional auxiliary sub-equation expansion method Mittag-Leffler function method |
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