指数有理函数法对非线性变阶分数微分方程的闭式求解

IF 1.9 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
Mashael M. ALBaidani, Umair Ali, Abdul Hamid Ganie
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引用次数: 0

摘要

分数微分方程的对称性特征可以有效解释自然界中的物理和生物现象。分数微分方程的广义形式是描述物理和生物应用的变阶分数微分方程。本文讨论了非线性时空变阶分数修正川原方程和(2 + 1)维伯格层次方程的闭式行波解。变阶分数微分方程有一个卡普托意义上的导数算子,通过分数变换转换成整数阶常微分方程(ODE)。用指数有理函数法求解得到的 ODE,并由此构建了新的精确解。提出了两个问题来确认时空变阶分数微分方程的解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The closed-form solution by the exponential rational function method for the nonlinear variable-order fractional differential equations
The symmetry features of fractional differential equations allow effective explanation of physical and biological phenomena in nature. The generalized form of the fractional differential equations is the variable-order fractional differential equations that describe the physical and biological applications. This paper discusses the closed-form traveling wave solutions for the nonlinear space–time variable-order fractional modified Kawahara and (2 + 1)-dimensional Burger hierarchy equations. The variable-order fractional differential equation has a derivative operator in the Caputo sense that is converted into the integer-order ordinary differential equation (ODE) by fractional transformation. The obtained ODE is solved by the exponential rational function method, and as a result, new exact solutions are constructed. Two problems are proposed to confirm the solutions of the space-time variable-order fractional differential equations.
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来源期刊
Frontiers in Physics
Frontiers in Physics Mathematics-Mathematical Physics
CiteScore
4.50
自引率
6.50%
发文量
1215
审稿时长
12 weeks
期刊介绍: Frontiers in Physics publishes rigorously peer-reviewed research across the entire field, from experimental, to computational and theoretical physics. This multidisciplinary open-access journal is at the forefront of disseminating and communicating scientific knowledge and impactful discoveries to researchers, academics, engineers and the public worldwide.
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