NEW APPLICATIONS OF THE FRACTIONAL DERIVATIVE TO EXTRACT ABUNDANT SOLITON SOLUTIONS OF THE TIME FRACTIONAL ZAKHAROV–KUZNETSOV–BENJAMIN–BONA–MAHONY EQUATION IN MATHEMATICAL PHYSICS

Amina Bibi (), Alina Alb Lupas (), Muhammad Abbas, Muhammad Kashif Iqbal (), Y. S. Hamed () and Miguel Vivas-Cortez
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Amina Bibi: Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan
Alina Alb Lupas: ��Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania
Muhammad Abbas: Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan
Muhammad Kashif Iqbal: Department of Mathematics, Government College University, Faisalabad, Pakistan
Y. S. Hamed: Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia
Miguel Vivas-Cortez: Faculty of Exact, Natural and Environmental Sciences, Ponticia Universidad Católica del Ecuador, FRACTAL (Fractional Research in Analysis, Convexity and Their Applications Laboratory), Av 12 de octubre 1076 y Roca, Apartado Quito 17-01-2184, Ecuador

FRACTALS (fractals), 2025, vol. 33, issue 08, 1-24

Abstract: This paper explores the time fractional Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZKBBM) equation as a framework for various phenomena, including water wave mechanics, shallow water waves, quantum mechanics, ion-acoustic waves in plasma, and electro-hydro-dynamical models for local electric fields and signal processing waves are transmitted over optical cables. Extended Direct Algebraic Technique (EDAT) and Improved Generalized Tanh-Coth Technique are used to find new accurate traveling-wave solutions with appropriate physical free parameter values. The fractional traveling-wave transformation is used to convert the equation into a nonlinear ordinary differential equation, where the fractional derivative is assessed in a conformable manner. Trigonometric and hyperbolic functions are the forms in which the solutions can be obtained. The suggested techniques can achieve periodic, mixed dark-bright soliton, bright soliton, dark soliton, M-shaped, Compacton soliton, bell-type soliton, smooth mixed dark-bright soliton and W-shaped soliton. Some of the obtained solutions are graphically represented as 3D and contour plots. Meanwhile, the impacts of the fractional parameter are shown in 2D plots. The above techniques are effective and reliable, and it may be utilized as a substitute to develop new solutions for many fractional differential equation types employed in mathematical physics.

Keywords: Time Fractional Zakharov–Kuznetsov–Benjamin–Bona–Mahony Equation; Extended Direct Algebraic Technique; Improved Generalized Tanh-Coth Technique; Solitons; Conformable Derivative (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25400912

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