Wave solutions for the (3+1)-dimensional fractional Boussinesq-KP-type equation using the modified extended direct algebraic method

Wafaa B. Rabie; Hamdy M. Ahmed; Taher A. Nofal; Soliman Alkhatib; Wafaa B. Rabie; Hamdy M. Ahmed; Taher A. Nofal; Soliman Alkhatib

doi:10.3934/math.20241532

AIMS Mathematics

2024, Volume 9, Issue 11: 31882-31897. doi: 10.3934/math.20241532

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Wave solutions for the (3+1)-dimensional fractional Boussinesq-KP-type equation using the modified extended direct algebraic method

1.
Department of Engineering Mathematics and Physics, Higher Institute of Engineering and Technology, Tanta, Egypt
2.
Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy, Cairo, Egypt
3.
Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
4.
College of Computer Information Technology, American University in the Emirates (AUE), Dubai intel Academic City, P.O. Box 503000, Dubai UAE

Received: 14 September 2024 Revised: 21 October 2024 Accepted: 28 October 2024 Published: 08 November 2024
MSC : 26A33, 35C07, 35C08, 76B15

In this study, we introduce the new (3+1)-dimensional $ \beta $-fractional Boussinseq-Kadomtsev-Petviashvili (KP) equation that describes the wave propagation in fluid dynamics and other physical contexts. By using the modified extended direct algebraic method, we investigate diverse wave solutions for the proposed fractional model. The acquired solutions, include (dark, bright) soliton, hyperbolic, rational, exponential, Jacobi elliptic function, and Weierstrass elliptic doubly periodic solutions. The primary objective is to investigate the influence of fractional derivatives on the characteristics and dynamics of wave solutions. Graphical illustrations are presented to demonstrate the distinct changes in the amplitude, shape, and propagation patterns of the soliton solutions as the fractional derivative parameters are varied.
- $ \beta $-fractional derivative,
- Boussinseq-Kadomtsev-Petviashvili equation,
- solitary solutions,
- analytic method
Citation: Wafaa B. Rabie, Hamdy M. Ahmed, Taher A. Nofal, Soliman Alkhatib. Wave solutions for the (3+1)-dimensional fractional Boussinesq-KP-type equation using the modified extended direct algebraic method[J]. AIMS Mathematics, 2024, 9(11): 31882-31897. doi: 10.3934/math.20241532

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Abstract

In this study, we introduce the new (3+1)-dimensional $ \beta $-fractional Boussinseq-Kadomtsev-Petviashvili (KP) equation that describes the wave propagation in fluid dynamics and other physical contexts. By using the modified extended direct algebraic method, we investigate diverse wave solutions for the proposed fractional model. The acquired solutions, include (dark, bright) soliton, hyperbolic, rational, exponential, Jacobi elliptic function, and Weierstrass elliptic doubly periodic solutions. The primary objective is to investigate the influence of fractional derivatives on the characteristics and dynamics of wave solutions. Graphical illustrations are presented to demonstrate the distinct changes in the amplitude, shape, and propagation patterns of the soliton solutions as the fractional derivative parameters are varied.

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