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

doi:10.1088/1674-1056/ab75c9

中国物理B ›› 2020, Vol. 29 ›› Issue (3): 30203-030203.doi: 10.1088/1674-1056/ab75c9

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

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

Hossam A. Ghany, Abd-Allah Hyder, M Zakarya

1 King Khalid University, College of Science, Department of Mathematics, P. O. Box 9004, 61413, Abha, Saudi Arabia;
2 Department of Engineering Mathematics and Physics, Faculty of Engineering, Al-Azhar University, 11371, Cairo, Egypt;
3 Department of Mathematics, Helwan University, Sawah Street(11282), Cairo, Egypt;
4 Department of Mathematics, Faculty of Science, Al-Azhar University, 71524, Assiut, Egypt

收稿日期:2019-07-07 修回日期:2019-10-15 出版日期:2020-03-05 发布日期:2020-03-05
通讯作者: Abd-Allah Hyder, M Zakarya E-mail:h.abdelghany@yahoo.com;mohammed_zakaria1983@yahoo.com

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

Hossam A. Ghany³, Abd-Allah Hyder^1,2, M Zakarya^1,4

1 King Khalid University, College of Science, Department of Mathematics, P. O. Box 9004, 61413, Abha, Saudi Arabia;
2 Department of Engineering Mathematics and Physics, Faculty of Engineering, Al-Azhar University, 11371, Cairo, Egypt;
3 Department of Mathematics, Helwan University, Sawah Street(11282), Cairo, Egypt;
4 Department of Mathematics, Faculty of Science, Al-Azhar University, 71524, Assiut, Egypt

Received:2019-07-07 Revised:2019-10-15 Online:2020-03-05 Published:2020-03-05
Contact: Abd-Allah Hyder, M Zakarya E-mail:h.abdelghany@yahoo.com;mohammed_zakaria1983@yahoo.com

摘要/Abstract

摘要： We deal with the Wick-type stochastic fractional Korteweg de-Vries (KdV) equation with conformable derivatives. With 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, Exp-function method

Abstract: We deal with the Wick-type stochastic fractional Korteweg de-Vries (KdV) equation with conformable derivatives. With 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.

Key words: Korteweg de-Vries (KdV) equation, conformable derivative, stochastic, Brownian motion, Exp-function method

中图分类号: (Partial differential equations)

02.30.Jr

02.50.Ey (Stochastic processes) 02.30.Gp (Special functions) 02.10.Ud (Linear algebra)

Hossam A. Ghany, Abd-Allah Hyder, M Zakarya. Exact solutions of stochastic fractional Korteweg de-Vries equation with conformable derivatives[J]. 中国物理B, 2020, 29(3): 30203-030203.

Hossam A. Ghany, Abd-Allah Hyder, M Zakarya. Exact solutions of stochastic fractional Korteweg de-Vries equation with conformable derivatives[J]. Chin. Phys. B, 2020, 29(3): 30203-030203.

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

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

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