Analytical wave solutions of an electronically and biologically important model via two efficient schemes

doi:10.1088/1674-1056/ace61f

中国物理B ›› 2023, Vol. 32 ›› Issue (11): 110201-110201.doi: 10.1088/1674-1056/ace61f

• • 下一篇

Analytical wave solutions of an electronically and biologically important model via two efficient schemes

Qingbo Huang^1,†, Asim Zafar², M. Raheel², and Ahmet Bekir^3,‡

1 Chongqing College of Architecture and Technology, Chongqing 401331, China;
2 Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Pakistan;
3 Neighbourhood of Akcaglan, Imarli Street, No. 28/4, Eskisehir 26030, Turkey

收稿日期:2023-05-26 修回日期:2023-06-18 接受日期:2023-07-11 出版日期:2023-10-16 发布日期:2023-10-16
通讯作者: Qingbo Huang, Ahmet Bekir E-mail:hw913987@126.com;bekirahmet@gmail.com

Analytical wave solutions of an electronically and biologically important model via two efficient schemes

Qingbo Huang^1,†, Asim Zafar², M. Raheel², and Ahmet Bekir^3,‡

1 Chongqing College of Architecture and Technology, Chongqing 401331, China;
2 Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Pakistan;
3 Neighbourhood of Akcaglan, Imarli Street, No. 28/4, Eskisehir 26030, Turkey

Received:2023-05-26 Revised:2023-06-18 Accepted:2023-07-11 Online:2023-10-16 Published:2023-10-16
Contact: Qingbo Huang, Ahmet Bekir E-mail:hw913987@126.com;bekirahmet@gmail.com

摘要/Abstract

摘要： We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh-Nagumo model with truncated M-fractional derivative, in which the exp_a function and extended sinh-Gordon equation expansion (EShGEE) schemes are utilized. The solutions obtained include dark, bright, dark-bright, periodic and other kinds of solitons. These analytical wave solutions are gained and verified with the use of Mathematica software. These solutions do not exist in literature. Some of the solutions are demonstrated by 2D, 3D and contour graphs. This model is mostly used in circuit theory, transmission of nerve impulses, and population genetics. Finally, both the schemes are more applicable, reliable and significant to deal with the fractional nonlinear partial differential equations.

关键词: spacetime fractional Fitzhugh-Nagumo model, truncated M-fractional derivative, exp_a function scheme, EShGEE scheme, analytical wave solutions

Abstract: We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh-Nagumo model with truncated M-fractional derivative, in which the exp_a function and extended sinh-Gordon equation expansion (EShGEE) schemes are utilized. The solutions obtained include dark, bright, dark-bright, periodic and other kinds of solitons. These analytical wave solutions are gained and verified with the use of Mathematica software. These solutions do not exist in literature. Some of the solutions are demonstrated by 2D, 3D and contour graphs. This model is mostly used in circuit theory, transmission of nerve impulses, and population genetics. Finally, both the schemes are more applicable, reliable and significant to deal with the fractional nonlinear partial differential equations.

Key words: spacetime fractional Fitzhugh-Nagumo model, truncated M-fractional derivative, exp_a function scheme, EShGEE scheme, analytical wave solutions

中图分类号: (Partial differential equations)

02.30.Jr

04.20.Jb (Exact solutions) 05.45.Yv (Solitons)

Qingbo Huang, Asim Zafar, M. Raheel, and Ahmet Bekir. Analytical wave solutions of an electronically and biologically important model via two efficient schemes[J]. 中国物理B, 2023, 32(11): 110201-110201.

Qingbo Huang, Asim Zafar, M. Raheel, and Ahmet Bekir. Analytical wave solutions of an electronically and biologically important model via two efficient schemes[J]. Chin. Phys. B, 2023, 32(11): 110201-110201.

参考文献

[1] Nilkanta D and Ray S S 2023 Opt. Quantum Electron. 55 328
[2] Nilkanta D and Ray S S 2022 Opt. Quantum Electron. 54 544
[3] Nilkanta D and Ray S S 2022 Opt. Quantum Electron. 54 112
[4] Ray S S and Nilkanta D 2022 Mod. Phys. Lett. B 36 2150544
[5] Rasool T, Hussain R, Al Sharif M, Mahmoud W and Osman M S 2023 Opt. Quantum Electron. 55 396
[6] Jaradat I, Sulaiman T A, Alshomrani A S, Yusuf A, Alquran M and Baleanu D 2023 Opt. Quantum Electron. 55 361
[7] Raza N, Arshed S, Khan K A and Baleanu D 2021 Mod. Phys. Lett. B 35 2150317
[8] Akbulut A, Taşcan F and Özel E 2012 Partial Different. Equ. Appl. Math. 4 100101
[9] Hosseini K, Akbulut A, Baleanu D and Salahshour S 2022 Commun. Theor. Phys. 74 025001
[10] Mirzazadeh M, Akbulut A, Tascan F and Akinyemi L 2022 Optik 252 168529
[11] Akbulut A and Kumar D 2023 Journal of Ocean Engineering and Science (in press)
[12] Raheel M, Inc M, Tala-Tebue E and Mahmoud K H 2022 Opt. Quantum Electron. 54 560
[13] Zafar A, Raheel M, Rezazadeh H, Inc M and Akinlar M A 2021 Opt. Quantum Electron. 53 604
[14] Rahman Z, Abdeljabbar A and Ali M Z 2022 Fractal and Fractional 6 444
[15] Shqair M, Alabedalhadi M, and Al-Omari S and Al-Smadi M 2022 Fractal and Fractional 6 252
[16] Ciancio A, Yel G, Kumar A, Baskonus H M and İlhan E 2022 Fractals 30 2240018
[17] Yan L, Baskonus H M, Cattani C and Gao W 2023 Math. Meth. Appl. Sci. (in press)
[18] Eslami M and Rezazadeh H 2016 Calcolo 53 475
[19] Rezazadeh H 2018 Optik 167 218
[20] Yao S W, Behera S, Inc M, Rezazadeh H, Virdi J P S, Mahmoud W, Arqub O A and Osman M S 2022 Results Phys. 42 105990
[21] Das P K, Mirhosseini-Alizamini S M, Gholamic D and Rezazadeh H 2023 Optik 283 170888
[22] Bekir A, Ayhan B and Ozer M N 2013 Chin. Phys. B 22 010202
[23] Ming S, Beidan W and Jun C 2020 Chin. Phys. B 29 100206
[24] Cai Q S, Dong M X and Zuo N Z 2017 Chin. Phys. B 26 100204
[25] Ahmad T A and Ezzat R H 2010 Appl. Math. Comput. 217 451
[26] Yan C 1996 Phys. Lett. A 224 77
[27] Zafar A, Bekir A, Raheel M and Rezazadeh H 2020 Int. J. Appl. Comput. Math. 6 65
[28] Zafar A, Raheel M, Hosseini K, Mirzazadeh M, Salahshour S, Park C and Shin D Y 2021 Results Phys. 31 104882
[29] Ali K K, Raheel M and Inc M 2022 Mod. Phys. Lett. B 36 2250089
[30] Zafar A, Bekir A, Raheel M and Razzaq W 2020 Optik 222 165355
[31] Kumar D, Manafian J, Hawlader F and Ranjbaran A 2018 Optik 160 159
[32] Cevikel A C, Bekir A, Abu Arqub O and Abukhaled M 2022 Front. Phys. 10 1028668
[33] Mohyud-Din S T, Khan Y, Faraz N and Yildirim A 2012 Int. J. Numer. Methods Heat Fluid Flow 22 335
[34] Tasbozan O and Kurt A 2020 Adiyaman University Journal of Science 10 256
[35] Tukur A S, Yel G and Bulut H 2019 Mod. Phys. Lett. B 32 1950052
[36] Sousa J V C and Oliveira C D E 2018 Int. J. Anal. Appl. 16 83
[37] Zayed E M E and Al-Nowehy A G 2017 J. Space Explor. 6 120
[38] Hosseini K, Ayati Z and Ansari R 2018 J. Mod. Opt. 65 847
[39] Zafar A 2019 Nonlinear Eng. 8 728
[40] Yang X L and Tang J S 2008 Commun. Theor. Phys. 50 1047

Analytical wave solutions of an electronically and biologically important model via two efficient schemes

Analytical wave solutions of an electronically and biologically important model via two efficient schemes

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Feng Yuan(袁丰), Behzad Ghanbari, Yongshuai Zhang(张永帅), and Abdul Majid Wazwaz. From breather solutions to lump solutions: A construction method for the Zakharov equation[J]. 中国物理B, 2023, 32(12): 120201-120201.
[2]	Wei Yang(杨薇), Xueping Cheng(程雪苹), Guiming Jin(金桂鸣), and Jianan Wang(王佳楠). Nondegenerate solitons of the (2+1)-dimensional coupled nonlinear Schrödinger equations with variable coefficients in nonlinear optical fibers[J]. 中国物理B, 2023, 32(12): 120202-120202.
[3]	Min-Yuan Liu(刘敏远), Hui Xu(许慧), and Zeng-Gui Wang(王增桂). Exact solutions of a time-fractional modified KdV equation via bifurcation analysis[J]. 中国物理B, 2023, 32(12): 120204-120204.
[4]	Jinzhou Liu(刘锦洲), Xinying Yan(闫鑫颖), Meng Jin(金梦), and Xiangpeng Xin(辛祥鹏). Darboux transformation, infinite conservation laws, and exact solutions for the nonlocal Hirota equation with variable coefficients[J]. 中国物理B, 2023, 32(12): 120401-120401.
[5]	Xi-Zhong Liu(刘希忠), Jie-Tong Li(李界通), and Jun Yu(俞军). Residual symmetry, CRE integrability and interaction solutions of two higher-dimensional shallow water wave equations[J]. 中国物理B, 2023, 32(11): 110206-110206.
[6]	Yarong Xia(夏亚荣), Kaikai Zhang(张开开), Ruoxia Yao(姚若侠), and Yali Shen(申亚丽). Trajectory equation of a lump before and after collision with other waves for generalized Hirota-Satsuma-Ito equation[J]. 中国物理B, 2023, 32(10): 100201-100201.
[7]	Xinying Yan(闫鑫颖), Jinzhou Liu(刘锦洲), and Xiangpeng Xin(辛祥鹏). Interaction solutions and localized waves to the (2+1)-dimensional Hirota-Satsuma-Ito equation with variable coefficient[J]. 中国物理B, 2023, 32(7): 70201-070201.
[8]	Li-Yang Xu(徐丽阳), Xiao-Jun Yin(尹晓军), Na Cao(曹娜) and Shu-Ting Bai(白淑婷). Soliton propagation for a coupled Schrödinger equation describing Rossby waves[J]. 中国物理B, 2023, 32(7): 70202-070202.
[9]	Jianan Liu(刘佳楠), Qingzhi Hou(侯庆志), Jianguo Wei(魏建国), and Zewei Sun(孙泽玮). ESR-PINNs: Physics-informed neural networks with expansion-shrinkage resampling selection strategies[J]. 中国物理B, 2023, 32(7): 70702-070702.
[10]	Hongcai Ma(马红彩), Xue Mao(毛雪), and Aiping Deng(邓爱平). Interaction solutions for the second extended (3+1)-dimensional Jimbo-Miwa equation[J]. 中国物理B, 2023, 32(6): 60201-060201.
[11]	Hangbing Shao(邵杭兵) and Bilige Sudao(苏道毕力格). Superposition formulas of multi-solution to a reduced (3+1)-dimensional nonlinear evolution equation[J]. 中国物理B, 2023, 32(5): 50204-050204.
[12]	Feng Yuan(袁丰) and Behzad Ghanbari. Positon and hybrid solutions for the (2+1)-dimensional complex modified Korteweg-de Vries equations[J]. 中国物理B, 2023, 32(4): 40201-040201.
[13]	W S Chung, A Gungor, J Kříž, B C Lütfüoǧlu, and H Hassanabadi. Conformable fractional heat equation with fractional translation symmetry in both time and space[J]. 中国物理B, 2023, 32(4): 40202-040202.
[14]	Sha Li(李莎), Tiecheng Xia(夏铁成), and Hanyu Wei(魏含玉). Riemann-Hilbert approach of the complex Sharma-Tasso-Olver equation and its N-soliton solutions[J]. 中国物理B, 2023, 32(4): 40203-040203.
[15]	Keyi Peng(彭珂依), Jing Yue(岳靖), Wen Zhang(张文), and Jian Li(李剑). Meshfree-based physics-informed neural networks for the unsteady Oseen equations[J]. 中国物理B, 2023, 32(4): 40207-040207.