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He’s Homotopy Perturbation Method and fractional complex transform for Analysis Time fractional Fornberg-Whitham Equation

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Sound & Vibration 2021年第4期55卷 295-303页

作者： Yanni Zhang Jing Pang College of Science Inner Mongolia University of TechnologyHohhot010000China Inner Mongolia Key Laboratory of Statistical Analysis Theory for Life Data and Neural Network Modeling Inner Mongolia University of TechnologyHohhot010000China

In this article,time fractional Fornberg-Whitham equation of He’s fractional derivative is *** transform the fractional model into its equivalent differential equation,the fractional complex transform is used and He’s homotopy perturbation method is implemented to get the approximate analytical solutions of the fractional-order *** graphs are plotted to analysis the fractional-order mathematical modeling.

关键词： Time fractional Fornberg-Whitham equation fractional complex transform He’s homotopy perturbation method

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New analytical exact solutions of time fractional KdV KZK equation by Kudryashov methods

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Chinese Physics B 2016年第4期25卷 30-36页

作者： S Saha Ray National Institute of Technology Department of Mathematics

In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov （KdV-KZK） equa- tion are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the non- linear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.

关键词： KdV-Khokhlov-Zabolotskaya-Kuznetsov equation Kudryashov method modified Kudryashovmethod fractional complex transform modified Riemann-Liouville derivative

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Exact Solutions for a Local fractional DDE Associated with a Nonlinear Transmission Line

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Communications in Theoretical Physics 2016年第9期65卷 315-320页

作者： smail Aslan Department of Mathematics zmir Institute of Technology

Of recent increasing interest in the area of fractional calculus and nonlinear dynamics are fractional differential-difference equations. This study is devoted to a local fractional differential-difference equation which is related to a nonlinear electrical transmission line. Explicit traveling wave solutions(kink/antikink solitons, singular,periodic, rational) are obtained via the discrete tanh method coupled with the fractional complex transform.

关键词： differential-difference equation local fractional derivative nonlinear transmission line discrete tanh method fractional complex transform

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