On soliton solutions of fractional-order nonlinear model appears in physical sciences

Naeem Ullah; Muhammad Imran Asjad; Jan Awrejcewicz; Taseer Muhammad; Dumitru Baleanu; Naeem Ullah; Muhammad Imran Asjad; Jan Awrejcewicz; Taseer Muhammad; Dumitru Baleanu

doi:10.3934/math.2022415

AIMS Mathematics

2022, Volume 7, Issue 5: 7421-7440. doi: 10.3934/math.2022415

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On soliton solutions of fractional-order nonlinear model appears in physical sciences

1.
Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan
2.
Department of Automation, Biomechanics, and Mechatronics, Faculty of Mechanical Engineering, Lodz University of Technology, Lodz 90924, Poland
3.
Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
4.
Department of Mathematics, Cankaya University, Balgat, Ankara, Turkey
5.
Institute of Space Sciences, Magurele, Bucharest, Romania
6.
Department of Medical Research, China Medical University Hospita, China Medical University, Taichung, Taiwan

Received: 29 November 2021 Revised: 04 January 2022 Accepted: 09 January 2022 Published: 14 February 2022
MSC : 35Q51, 35Q53

In wave theory, the higher dimensional non-linear models are very important to define the physical phenomena of waves. Herein study we have built the various solitons solutions of (4+1)-dimensional fractional-order Fokas equation by using two analytical techniques that is, the Sardar-subequation method and new extended hyperbolic function method. Different types of novel solitons are attained such as, singular soliton, bright soliton, dark soliton, and periodic soliton. To understand the physical behavior, we have plotted 2D and 3D graphs of some selected solutions. From results we concluded that the proposed methods are straightforward, simple, and efficient. Moreover, this paper offers a hint, how we can convert the fractional-order PDE into an ODE to acquire the exact solutions. Also, the proposed methods and results can be help to examine the advance fractional-order models which seem in optics, hydrodynamics, plasma and wave theory etc.
- Fokas equation,
- Sardar-subequation method,
- new extended hyperbolic function method,
- solitons solutions
Citation: Naeem Ullah, Muhammad Imran Asjad, Jan Awrejcewicz, Taseer Muhammad, Dumitru Baleanu. On soliton solutions of fractional-order nonlinear model appears in physical sciences[J]. AIMS Mathematics, 2022, 7(5): 7421-7440. doi: 10.3934/math.2022415

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Abstract

In wave theory, the higher dimensional non-linear models are very important to define the physical phenomena of waves. Herein study we have built the various solitons solutions of (4+1)-dimensional fractional-order Fokas equation by using two analytical techniques that is, the Sardar-subequation method and new extended hyperbolic function method. Different types of novel solitons are attained such as, singular soliton, bright soliton, dark soliton, and periodic soliton. To understand the physical behavior, we have plotted 2D and 3D graphs of some selected solutions. From results we concluded that the proposed methods are straightforward, simple, and efficient. Moreover, this paper offers a hint, how we can convert the fractional-order PDE into an ODE to acquire the exact solutions. Also, the proposed methods and results can be help to examine the advance fractional-order models which seem in optics, hydrodynamics, plasma and wave theory etc.

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