A COMPARATIVE ANALYSIS REPORT ON THE MULTI-WAVE FRACTIONAL HIROTA EQUATION IN NONLINEAR DISPERSIVE MEDIA

Xiangjun Gao, Waqas Ali Faridi, Muhammad Imran Asjad, Adil Jhangeer, Maryam Aleem and Mohammad Mahtab Alam
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Xiangjun Gao: Nanchang Institute of Technology, Nanchang 330044, P. R. China2School of Computer Science and Technology, Xuzhou University of Technology, Xuzhou 221018, P. R. China
Waqas Ali Faridi: Department of Mathematics, University of Management and Technology, Lahore, Pakistan
Muhammad Imran Asjad: Department of Mathematics, University of Management and Technology, Lahore, Pakistan
Adil Jhangeer: Department of Mathematics, Namal University, Talagang Road, Mianwali 42250, Pakistan
Maryam Aleem: Department of Mathematics, University of Management and Technology, Lahore, Pakistan
Mohammad Mahtab Alam: Department of Basic Medical Sciences, College of Applied Medical Science, King Khalid University, Abha 61421, Saudi Arabia

FRACTALS (fractals), 2022, vol. 30, issue 08, 1-16

Abstract: The propagation attributes of waves and its modeling maneuvers have a significant role in maritime, coastal engineering, and ocean. In the geographical fields, waves are primary source of environmental process owed to energy conveyance on the floating structure or on the synthetic field. This study aims to investigate the new auxiliary equation method to obtain analytical solutions of the nonlinear Hirota model with fractional order. The fractional model is developed by utilizing Riemann–Liouville, 𠔅, and the fractional-order Atangana–Baleanu differential operator in Riemann–Liouville sense. The solitonic patterns of the nonlinear fractional Hirota equation successfully surveyed, where the exact solutions are presented by rational, trigonometric, hyperbolic, and exponential functions. The contravene of surveyed results with the substantially recognized result is executed which states the novelty of obtained results. Three dimensional as well as two-dimensional comparison is presented for a couple of Hirota model solutions which are revealed diagrammatically for appropriate parameters by using Mathematica. We strongly believe that this study will help physicists to predict some new conceptions in the field of mathematical physics.

Keywords: Fractional Derivatives; Multi-wave Nonlinear Hirota Equation; New Auxiliary Equation Method; Traveling Wave Transformation; Soliton Solutions (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402265

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