Solutions of Some Linear Fractional Partial Differential Equations in Mathematical Physics

Q4 Mathematics

Journal of the Indian Mathematical Society Pub Date : 2018-06-01 DOI:10.18311/JIMS/2018/20144

Ranjit R. Dhunde, G. L. Waghmare

引用次数: 6

Abstract

In this article, we use double Laplace transform method to find solution of general linear fractional partial differential equation in terms of Mittag-Leffler function subject to the initial and boundary conditions. The efficiency of the method is illustrated by considering fractional wave and diffusion equations, Klein-Gordon equation, Burger’s equation, Fokker-Planck equation, KdV equation, and KdV-Burger’s equation of mathematical physics.

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数学物理中若干线性分数阶偏微分方程的解

在本文中，我们使用双拉普拉斯变换方法，在初始条件和边界条件下，用Mittag-Leffler函数求解一般线性分式偏微分方程。通过考虑分数波和扩散方程、Klein-Gordon方程、Burger方程、Fokker-Planck方程、KdV方程和数学物理的KdV-Burger方程，说明了该方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of the Indian Mathematical Society Mathematics-Mathematics (all)

CiteScore

0.50

自引率

0.00%

发文量

期刊介绍： The Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onwards,it is published as its current title ''the Journal of Indian Mathematical Society. The four issues of the Journal constitute a single volume and it is published in two parts: issues 1 and 2 (January to June) as one part and issues 3 and 4 (July to December) as the second part. The four issues of the Mathematics Student (another periodical of the Society) are published as a single yearly volume. Only the original research papers of high quality are published in the Journal of Indian Mathematical Society.