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

doi:10.1088/1674-1056/ab75c9

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.

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

Received: 07 July 2019
Revised: 15 October 2019
Accepted manuscript online:

PACS:	02.30.Jr	(Partial differential equations)
	02.50.Ey	(Stochastic processes)
	02.30.Gp	(Special functions)
	02.10.Ud	(Linear algebra)

Corresponding Authors: Abd-Allah Hyder, M Zakarya
E-mail: h.abdelghany@yahoo.com;mohammed_zakaria1983@yahoo.com

Cite this article:

Hossam A. Ghany, Abd-Allah Hyder, M Zakarya Exact solutions of stochastic fractional Korteweg de-Vries equation with conformable derivatives 2020 Chin. Phys. B 29 030203

[1]	Abdeljawad T 2015 J. Comput. Appl. Math. 279 57
[2]	Baskonus H M and Gómez-Aguilar J F 2019 Mod. Phys. Lett. B 33 1950251
[3]	Benkhettoua N, Hassania S and Torres D F M 2016 J. King Saud Univ. Sci. 28 93
[4]	Çenesiz Y, Baleanu D, Kurt A and Tasbozan O 2017 Waves in Random and Complex Media 27 103
[5]	Chen B and Xie Y 2005 Chaos Soliton. Fract. 23 281
[6]	Chen B and Xie Y C 2006 J. Comput. Appl. Math. 197 345
[7]	Chen B and Xie Y C 2007 J. Comput. Appl. Math. 203 249
[8]	Chung W S 2015 J. Comput. Appl. Math. 290 150
[9]	Eslami M and Rezazadeh H 2016 Calcolo 53 475
[10]	Ghanbaria B and Gómez-Aguilarb J F 2019 Revista Mexicana de Física 65 73
[11]	Ghanbaria B and Gómez-Aguilarb J F 2019 Mod. Phys. Lett. B 33 1950235
[12]	Ghany H A and Hyder A 2012 International Review of Physics 6 153
[13]	Ghany H A, Okb El Babb A S, Zabel A M and Hyder A 2013 Chin. Phys. B 22 080501
[14]	Ghany H A and Hyder A 2014 Int. J. Math. Analysis 23 2199
[15]	Ghany H A and Hyder A 2014 Chin. Phys. B 23 060503
[16]	Ghany H A and Hyder A 2014 Kuwait Journal of Science 41 75
[17]	Gökdoğan A, Ünal E and Çelik E 2016 Miskolc Math. Notes 17 267
[18]	Hammad M A and Khalil R 2014 Int. J. Pure Appl. Math. 94 215
[19]	He J H and Wu X H 2006 Chaos Soliton. Fract. 30 700
[20]	He J H and Abdou M A 2007 Chaos Soliton. Fract. 34 1421
[21]	He J H 2008 Int. J. Mod. Phys. B 22 3487
[22]	Hereman W 2009 Shallow water waves and solitary waves, Encyclopedia of Complexity and Systems Science (R. A. Meyers Ed.) (Heibelberg: Springer Verlag) pp. 1620-1536
[23]	Holden H, Øsendal B, Ubøe J and Zhang T 2010 Stochastic partial differential equations (New York: Springer Science+Business Media, LLC)
[24]	Hyder A 2017 Journal of Mathematical Sciences: Advances and Applications 45 1
[25]	Hyder A 2018 Pioneer Journal of Advances in Applied Mathematics 24 39
[26]	Hyder A and Zakarya M 2016 Int. J. Pure Appl. Math. 109 539
[27]	Hyder A Zakarya M 2019 Journal of the Egyptian Mathematical Society 27 5
[28]	Jiao X Y 2018 Chin. Phys. B 27 100202
[29]	Khalil R, Al Horani M, Yousef A. and Sababheh M A 2014 J. Comput. Appl. Math. 246 65
[30]	Khusnutdinova K R, Stepanyants Y A and Tranter M R 2018 Phys. Fluids 30 022104
[31]	Kumarab D, Seadawy R A and Joardare A K 2018 Chin. J. Phys. 56 75
[32]	Kudryashov N A and Loguinova N B Commun. Nonlinear Sci. Numer. Simul. 14 1881
[33]	Liu X Z, Yu J, Lou Z M et al. 2019 Chin. Phys. B 28 010201
[34]	Pérez J E S, Gómez-Aguilar J F, D. Baleanu and F. Tchier 2018 Entropy 20 384
[35]	Qian C, Rao J G, Liu Y B, et al. 2016 Chin. Phys. Lett. 33 110201
[36]	Taogetusang and Sirendaoerji 2006 Chin. Phys. B 15 1143
[37]	Wadati M 1983 J. Phys. Soc. Jpn. 52 2642
[38]	Wazwaz A M 2018 Mathematical Methods in the Applied Sciences 41 80
[39]	Hu X R, Chen J C and Chen Y 2015 Chin. Phys. Lett. 32 070201
[40]	Xie Y C 2003 Phys. Lett. A 310 161
[41]	Xu S Q and Geng X G 2018 Chin. Phys. B 27 120202
[42]	Yuliawati L Budhi W S and Adytia D 2019 J. Phys.: Conf. Ser. 1127 012065
[43]	Yépez-Martínez H and Gómez-Aguilar J F 2019 Waves in Random and Complex Media 29 678
[44]	Yépez-Martínez H, Gómez-Aguilar J F and Atangana A 2018 Math. Model. Nat. Phenom. 13 14
[45]	Yépez-Martínez H, Gómez-Aguilar J F and Baleanu D 2018 Optik 155 357
[46]	Yépez-Martínez H and Gómez-Aguilar J F 2019 Waves in Random and Complex Media
[47]	Zhang S 2007 Phys. Lett. A 365 448
[48]	Zheng P and Jia M 2018 Chin. Phys. B 27 120201
[49]	Zhu S D 2007 Int. J. Nonlinear Sci. Numer. Simul. 8 465

[1]	Inverse stochastic resonance in modular neural network with synaptic plasticity Yong-Tao Yu(于永涛) and Xiao-Li Yang(杨晓丽). Chin. Phys. B, 2023, 32(3): 030201.
[2]	Realizing reliable XOR logic operation via logical chaotic resonance in a triple-well potential system Huamei Yang(杨华美) and Yuangen Yao(姚元根). Chin. Phys. B, 2023, 32(2): 020501.
[3]	Inhibitory effect induced by fractional Gaussian noise in neuronal system Zhi-Kun Li(李智坤) and Dong-Xi Li(李东喜). Chin. Phys. B, 2023, 32(1): 010203.
[4]	Physical aspects of magnetized Jeffrey nanomaterial flow with irreversibility analysis Fazal Haq, Muhammad Ijaz Khan, Sami Ullah Khan, Khadijah M Abualnaja, and M A El-Shorbagy. Chin. Phys. B, 2022, 31(8): 084703.
[5]	Hyperparameter on-line learning of stochastic resonance based threshold networks Weijin Li(李伟进), Yuhao Ren(任昱昊), and Fabing Duan(段法兵). Chin. Phys. B, 2022, 31(8): 080503.
[6]	Ratchet transport of self-propelled chimeras in an asymmetric periodic structure Wei-Jing Zhu(朱薇静) and Bao-Quan Ai(艾保全). Chin. Phys. B, 2022, 31(4): 040503.
[7]	Dynamics and intermittent stochastic stabilization of a rumor spreading model with guidance mechanism in heterogeneous network Xiaojing Zhong(钟晓静), Yukun Yang(杨宇琨), Runqing Miao(苗润青), Yuqing Peng(彭雨晴), and Guiyun Liu(刘贵云). Chin. Phys. B, 2022, 31(4): 040205.
[8]	Stochastic optimal control for norovirus transmission dynamics by contaminated food and water Anwarud Din and Yongjin Li(黎永锦). Chin. Phys. B, 2022, 31(2): 020202.
[9]	Dynamical behavior and optimal impulse control analysis of a stochastic rumor spreading model Liang'an Huo(霍良安) and Xiaomin Chen(陈晓敏). Chin. Phys. B, 2022, 31(11): 110204.
[10]	Dynamics of a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise Liang-An Huo(霍良安), Ya-Fang Dong(董雅芳), and Ting-Ting Lin(林婷婷). Chin. Phys. B, 2021, 30(8): 080201.
[11]	A sign-function receiving scheme for sine signals enhanced by stochastic resonance Zhao-Rui Li(李召瑞), Bo-Hang Chen(陈博航), Hui-Xian Sun(孙慧贤), Guang-Kai Liu(刘广凯), and Shi-Lei Zhu(朱世磊). Chin. Phys. B, 2021, 30(8): 080502.
[12]	Collective stochastic resonance behaviors of two coupled harmonic oscillators driven by dichotomous fluctuating frequency Lei Jiang(姜磊), Li Lai(赖莉), Tao Yu(蔚涛), Maokang Luo(罗懋康). Chin. Phys. B, 2021, 30(6): 060502.
[13]	Time-varying coupling-induced logical stochastic resonance in a periodically driven coupled bistable system Yuangen Yao(姚元根). Chin. Phys. B, 2021, 30(6): 060503.
[14]	Stationary response of colored noise excited vibro-impact system Jian-Long Wang(王剑龙), Xiao-Lei Leng(冷小磊), and Xian-Bin Liu(刘先斌). Chin. Phys. B, 2021, 30(6): 060501.
[15]	Near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters Liang'an Huo(霍良安) and Xiaomin Chen(陈晓敏). Chin. Phys. B, 2021, 30(12): 120205.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

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

Cite this article:

Online attention