Exact solution of time-fractional partial differential equations using Laplace transform

Naser Al-Qutaifi

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Exact solution of time-fractional partial differential equations using Laplace transform

机译：使用拉普拉斯变换的时间分数阶偏微分方程的精确解

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The idea of replacing the first derivative in time by a fractional derivative of order , where , leads to a fractional generalization of any partial differential equations of integer order. In this paper, we obtain a relationship between the solution of the integer order equation and the solution of its fractional extension by using the Laplace transform method.

机译：用阶次的分数导数及时替换一阶导数的想法导致对整数阶的任何偏微分方程的分数泛化。在本文中，我们通过使用Laplace变换方法获得了整数阶方程的解及其分数阶扩展的解之间的关系。

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《International Journal of Basic and Applied Sciences》 |2016年第1期|共4页
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Naser Al-Qutaifi;
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1. Exact Solution of Time-Fractional Partial Differential Equations Using Sumudu Transform [J] . ABDOLAMIR KARBALAIE, MOHAMMAD MEHDI MONTAZERI, HAMED HAMID MUHAMMED WSEAS Transactions on Mathematics . 2014,第Pta1期

机译：利用Sumudu变换精确求解时分形偏微分方程
2. Exact solutions of some nonlinear partial differential equations using the variational iteration method linked with Laplace transforms and the Pade technique [J] . Tamer A. Abassy, Magdy A. El-Tawil, H. El-Zoheiry Computers & mathematics with applications . 2007,第7a8期

机译：与拉普拉斯变换和Pade技术相联系的变分迭代方法对某些非线性偏微分方程的精确解
3. A numerical method using Laplace-like transform and variational theory for solving time-fractional nonlinear partial differential equations with proportional delay [J] . Bekela Alemu Senbeta, Belachew Melisew Tefera, Wole Getinet Alemayehu Advances in Difference Equations . 2020,第a期

机译：一种数值方法，使用LAPLACS样变换和变分理论用比例延迟求解时间分数非线性偏微分方程
4. Positive Solution for P-laplace Problems with Nonlinear Time-fractional Differential Equation [C] . Shifeng Zhang, Zhiyang Jia, Jihe Wang, International Conference on Modelling, Simulation and Applied Mathematics . 2015

机译：非线性时间分数微分方程的P-LAPLACE问题的正解
5. n-dimensional Laplace transformations and their applications in partial differential equations. [D] . Saberi-Nadjafi, Jafar. 1993

机译：n维拉普拉斯变换及其在偏微分方程中的应用。
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 some nonlinear partial differential equations using the variational iteration method linked with Laplace transforms and the Padé technique [O] . Abassy Tamer A., El-Tawil Magdy A., El-Zoheiry H. 2007

机译：与Laplace变换和Padé技术联系在一起的变分迭代方法对某些非线性偏微分方程的精确解

Exact solution of time-fractional partial differential equations using Laplace transform

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