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The generalized differential transform method for solution of a free vibration linear differential equation with fractional derivative damping

机译：具有分数衍生阻尼的自由振动线性微分方程溶液的广义差分变换方法

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Deepanjan Das;
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1. In this paper, we implement the fractional complex transform method to convert the nonlinear fractional Klein-Gordon equation (FKGE) to an ordinary differential equation. We use the variational iteration method (VIM) to solve the resulting ODE. The fractional derivatives are presented in terms of the Caputo sense. Some numerical examples are presented to validate the proposed techniques. Finally, a comparison with the numerical solution using Runge-Kutta of order four is given. [J] . M. M. Khader, M. Adel Nonlinear engineering: Modeling and application . 2016,第3期

机译：在本文中，我们采用分数阶复杂变换方法将非线性分数阶Klein-Gordon方程（FKGE）转换为常微分方程。我们使用变分迭代方法（VIM）来解决所得的ODE。分数导数以Caputo形式表示。提出了一些数值例子来验证所提出的技术。最后，与使用四阶Runge-Kutta的数值解进行了比较。
2. Analytical Solution with Tanh-Method and Fractional Sub-Equation Method for Non-Linear Partial Differential Equations and Corresponding Fractional Differential Equation Composed With Jumarie Fractional Derivative [J] . Uttam Ghosh, Srijan Sengupta, Susmita Sarkar, International Journal of Applied Mathematics & Statistics . 2016,第3期

机译：非线性偏微分方程及其对应的分数阶微分方程与Jumarie分数阶导数组成的Tanh方法和分数次方程方法的解析解
3. Approximate solutions of nonlinear fractional Kolmogorov-Petrovskii- Piskunov equations using an enhanced algorithm of the generalized two-dimensional differential transform method [J] . Song L.-N., Wang W.-G. Communications in Theoretical Physics . 2012,第2期

机译：非线性分数阶Kolmogorov-Petrovskii-Piskunov方程的近似解，使用广义二维差分变换方法的改进算法
4. Solving fractional partial differential equations in fluid mechanics by generalized differential transform method [C] . Xuehui Chen, Liang Wei, Jizhe Sui, 2011 International Conference on Multimedia Technology . 2011

机译：用广义微分变换法求解流体力学中的分数阶偏微分方程
5. Power series solutions of fractional differential equations and symbolic derivatives and integrals. [D] . Benghorbal, Mhenni M. 2004

机译：分数阶微分方程和符号导数与积分的幂级数解。
6. A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations [O] . Brahim Benhammouda, Hector Vazquez-Leal -1

机译：微分变换方法的一种新的多步技术用于求解某些非线性可变时滞微分方程的解析解
7. A comparison between numerical solutions to fractional differential equations: Adams-type predictor-corrector and multi-step generalized differential transform method [O] . Momenzadeh, Alireza, Ahrabi, Sima Sarv 2017

机译：分数阶微分数值解的比较方程：adams型预测校正器和多步广义差分变换方法

The generalized differential transform method for solution of a free vibration linear differential equation with fractional derivative damping

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