Lump-type kink wave phenomena of the space-time fractional phi-four equation

Khudhayr A. Rashedi; Musawa Yahya Almusawa; Hassan Almusawa; Tariq S. Alshammari; Adel Almarashi; Khudhayr A. Rashedi; Musawa Yahya Almusawa; Hassan Almusawa; Tariq S. Alshammari; Adel Almarashi

doi:10.3934/math.20241637

AIMS Mathematics

2024, Volume 9, Issue 12: 34372-34386. doi: 10.3934/math.20241637

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Lump-type kink wave phenomena of the space-time fractional phi-four equation

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 55476, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Kingdom of Saudi Arabia

Received: 18 October 2024 Revised: 18 November 2024 Accepted: 22 November 2024 Published: 05 December 2024
MSC : 34G20, 35A20, 35A22, 35R11

This article examines the space-time fractional phi-four (PF) model which is an improvement of the Klein-Fock-Gordon (KFG) model that is relevant in quantum mechanics, transmission of ultra-short pulses in optical fibers, de Broglie wave duality, and compound particles in spinless relativistic systems. New solitary wave solutions of the fractional phi-four equation were found with the help of the Riccati-Bernoulli sub-ODE method together with the Bäcklund transformation. The conformable fractional derivative played the role of improving the modeling of the complex dynamical systems. The obtained solutions, which were illustrated by giving 2D, 3D MATLAB plots and contour illustrations, were s eful in nuclear, particle physics and fluid mechanics. Thus, the current work demonstrates the applicability of the proposed approach in handling the fractional order deviations and contributes to the investigation of the dynamic behavior of the PF model.
- Bäcklund transformation,
- fractional phi-four (PF),
- Riccatti equation,
- symbolic computation,
- solitary wave solutions
Citation: Khudhayr A. Rashedi, Musawa Yahya Almusawa, Hassan Almusawa, Tariq S. Alshammari, Adel Almarashi. Lump-type kink wave phenomena of the space-time fractional phi-four equation[J]. AIMS Mathematics, 2024, 9(12): 34372-34386. doi: 10.3934/math.20241637

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Abstract

This article examines the space-time fractional phi-four (PF) model which is an improvement of the Klein-Fock-Gordon (KFG) model that is relevant in quantum mechanics, transmission of ultra-short pulses in optical fibers, de Broglie wave duality, and compound particles in spinless relativistic systems. New solitary wave solutions of the fractional phi-four equation were found with the help of the Riccati-Bernoulli sub-ODE method together with the Bäcklund transformation. The conformable fractional derivative played the role of improving the modeling of the complex dynamical systems. The obtained solutions, which were illustrated by giving 2D, 3D MATLAB plots and contour illustrations, were s eful in nuclear, particle physics and fluid mechanics. Thus, the current work demonstrates the applicability of the proposed approach in handling the fractional order deviations and contributes to the investigation of the dynamic behavior of the PF model.

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