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Abundant solutions of Wick-type stochastic fractional 2D KdV equations

Chinese Physics B 2014年第6期23卷 97-103页

作者： hossam a.ghany Abd-Allah Hyder Department of Mathematics Faculty of Science Taif University Department of Mathematics Helwan University Department of Engineering Physics and Mathematics Faculty of Engineering Al-Azhar University

A modified fractional sub-equation method is applied to Wick-type stochastic fractional two-dimensional （2D） KdV equations. With the help of a Hermit transform, we obtain a new set of exact stochastic solutions to Wick-type stochastic fractional 2D KdV equations in the white noise space. These solutions include exponential decay wave solutions, soliton wave solutions, and periodic wave solutions. Two examples are explicitly given to illustrate our approach.

关键词： 2D KdV equations fractional calculus white noise Hermite transform

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Exact solutions of stochastic fractional Korteweg de–Vries equation with conformable derivatives

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Chinese Physics B 2020年第3期29卷 62-69页

作者： hossam a.ghany Abd-Allah Hyder M Zakarya King Khalid University College of ScienceDepartment of MathematicsP.O.Box 900461413AbhaSaudi Arabia Department of Engineering Mathematics and Physics Faculty of EngineeringAl-Azhar University11371CairoEgypt Department of Mathematics Helwan UniversitySawah Street(11282)CairoEgypt Department of Mathematics Faculty of ScienceAl-Azhar University71524AssiutEgypt

We deal with the Wick-type stochastic fractional Korteweg de–Vries(KdV) equation with conformable *** the aid of the Exp-function method, white noise theory, and Hermite transform, we produce a novel set of exact soliton and periodic wave solutions to the fractional KdV equation with conformable derivatives. With the help of inverse Hermite transform, we get stochastic soliton and periodic wave solutions of the Wick-type stochastic fractional KdV equation with conformable derivatives. Eventually, by an application example, we show how the stochastic solutions can be given as Brownian motion functional solutions.

关键词： Korteweg de–Vries(KdV)equation conformable derivative stochastic Brownian motion Expfunction method

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Analytical Approach to Exact Solutions for the Wick-Type Stochastic Space-Time Fractional KdV Equation

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Chinese Physics Letters 2014年第6期31卷 29-33页

作者： hossam A. ghany Department of Mathematics Faculty of Industrial Education Ameria (11282) Helwan University Cairo Egypt Department of Mathematics Faculty of Science Taif University Hawea(888) Tail Saudi Arabia

This study is devoted to giving an analytical approach to exact solutions for the Wick-type stochastic spacetime fractional KdV equation. By means of Hermite transform, white noise theory, and the fractional Riccati equation method, we derive white noise functional solutions for the Wick-type stochastic space-time fractional KdV equations. Exact traveling wave solutions for the variable coefficients space-time fractional KdV equations are given by using the fractional Riccati equation method. The obtained results include soliton-like, periodic, and rational solutions.

关键词： Riccati equations

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The fractional coupled KdV equations: Exact solutions and white noise functional approach

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Chinese Physics B 2013年第8期22卷 302-308页

作者： hossam A. ghany A. S. Okb El Bab A. M. Zabel Abd-Allah Hyder Department of Mathematics Faculty of Science Taif UniversityTaif Saudi Arabia Department of Mathematics Faculty of Industrial Education Helwan UniversityCairo Egypt Department of Mathematics Faculty of Science Al-Azhar UniversityCairo Egypt Department of Physics and Mathematics Faculty of Engineering Al-Azhar UniversityCairo Egypt

Variable coefficients and Wick-type stochastic fractional coupled KdV equations are investigated. By using the mod- ified fractional sub-equation method, Hermite transform, and white noise theory the exact travelling wave solutions and white noise functional solutions are obtained, including the generalized exponential, hyperbolic, and trigonometric types.

关键词： coupled KdV equations fractional calculus white noise Hermite transform

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