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

Uttam Ghosh; Srijan Sengupta; Susmita Sarkar; Shantanu Das

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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

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

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The solution of non-linear differential equation, non-linear partial differential equation and non-linear fractional differential equation is current research in Applied Science. Here tanh-method and Fractional Sub-Equation methods are used to solve three non-linear differential equations and the corresponding fractional differential equation. The fractional differential equations here are composed with Jumarie fractional derivative. Both the solution is obtained in analytical traveling wave solution form. We have not come across solutions of these equations reported anywhere earlier.

机译：非线性微分方程，非线性偏微分方程和非线性分数阶微分方程的求解是应用科学领域的最新研究。在此，tanh方法和分数次方程方法用于求解三个非线性微分方程和相应的分数微分方程。分数阶微分方程由Jumarie分数阶导数组成。两种解均以解析行波解形式获得。我们没有在较早的地方遇到过这些方程的解。

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《International Journal of Applied Mathematics & Statistics》 |2016年第3期|共21页
作者
Uttam Ghosh; Srijan Sengupta; Susmita Sarkar; Shantanu Das;
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正文语种 eng
中图分类计量学;
关键词
Tanh-method; Fractional Sub-Equation Method; Boussinesq equation; Non-linear Evolution equation; Fractional Differential Equation; Jumarie Fractional Derivative;

机译：Tanh法;分数阶子方程法;Boussinesq方程;非线性演化方程;分数阶微分方程;Jumarie分数阶导数;

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1. 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
2. Exact solutions of non-linear fractional partial differential equations by fractional sub-equation method [J] . Ma Hong-Cai, Yao Dan-Dan, Peng Xiao-Fang Thermal science . 2015,第4期

机译：分数阶子方程法求解非线性分数阶偏微分方程的精确解
3. Explicit solutions for space-time fractional partial differential equations in mathematical physics by a new generalized fractional Jacobi elliptic equation-based sub-equation method [J] . Feng Qinghua, Meng Fanwei Optik: Zeitschrift fur Licht- und Elektronenoptik: = Journal for Light-and Electronoptic . 2016,第19期

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4. A generalized fractional sub-equation method for nonlinear fractional differential equations [C] . Ahmet Bekir, Esin Aksoy, ?zkan Güner International Conference on Analysis and Applied Mathematics . 2014

机译：非线性分数微分方程的广义分数次方程方法
5. Fractional derivatives, fractional differential equations, and their numerical approximation [D] . Hatcher, Christopher 2013

机译：分数阶导数，分数阶微分方程及其数值逼近
6. Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations [O] . Rasool Shah, Hassan Khan, Muhammad Arif, 2019

机译：拉普拉斯 - adomian分解方法在三阶分散分数偏微分方程分析解的应用
7. EXACT SOLUTIONS OF NON-LINEAR FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS BY FRACTIONAL SUB-EQUATION METHOD [O] . Hong-cai Ma A, Dan-dan Yao A, Xiao-fang Peng A 2016

机译：用分数次方程法精确求解非线性分数阶微分方程

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

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