NOVEL TRAVELING-WAVE SOLUTIONS OF SPATIAL-TEMPORAL FRACTIONAL MODEL OF DYNAMICAL BENJAMIN–BONA–MAHONY SYSTEM

Mohammed Al-Smadi, Shrideh Al-Omari, Sharifah Alhazmi, Yeliz Karaca and Shaher Momani
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Mohammed Al-Smadi: College of Commerce and Business, Lusail University, Lusail, Doha, Qatar¶Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE
Shrideh Al-Omari: ��Department of Scientific Basic Sciences, Faculty of Engineering Technology, Al-Balqa Applied University, Amman, Jordan
Sharifah Alhazmi: ��Mathematics Department, Al-Qunfudah University College, Umm Al-Qura University, Mecca 21955, Kingdom of Saudi Arabia
Yeliz Karaca: �Chan Medical School (UMASS), University of Massachusetts, 55 Lake Avenue North, Worcester, MA 01655, USA
Shaher Momani: �Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE∥Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan

FRACTALS (fractals), 2023, vol. 31, issue 10, 1-23

Abstract: This paper investigates the dynamics of exact traveling-wave solutions for nonlinear spatial and temporal fractional partial differential equations with conformable order derivatives arising in nonlinear propagation waves of small amplitude including nonlinear fractional modified Benjamin–Bona–Mahony equation, fractional Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation and fractional (2+1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation as well. By utilizing the Sine-Gordon expansion method (SGEM), new real- and complex-valued exact traveling-wave solutions are reported by preferring suitable values of physical free parameters. The nonlinear governing equations are reduced into auxiliary nonlinear ordinary differential equations with aid of fractional traveling-wave transformation, in which the fractional derivative is evaluated in a conformable sense. The productivity process of the proposed method for predicting the desirable solutions is also provided. Some of the obtained solutions are simulated graphically in 3D and contour plots. Meanwhile, the effects of the fractional parameter α in the space and the time direction are illustrated in 2D plots to ensure the novelty, applicability and credibility of the SGEM. These results reveal that the suggested method is general and adequate for dealing with nonlinear models featuring fractional derivatives and can be employed to analyze wide classes of complex phenomena of partial differential equations occurring in engineering and nonlinear dynamics.

Keywords: Nonlinear Partial Differential Equation; Traveling Wave Solution; Fractional Benjamin–Bona–Mahony Family; Sine–Gordon Expansion Method; Conformable Derivative (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23401898

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