Efficient solutions for time fractional Sawada-Kotera, Ito, and Kaup-Kupershmidt equations using an analytical technique

Humaira Yasmin; Aljawhara H. Almuqrin; Humaira Yasmin; Aljawhara H. Almuqrin

doi:10.3934/math.2024994

AIMS Mathematics

2024, Volume 9, Issue 8: 20441-20466. doi: 10.3934/math.2024994

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Efficient solutions for time fractional Sawada-Kotera, Ito, and Kaup-Kupershmidt equations using an analytical technique

Humaira Yasmin ^{1,2
,
,},
Aljawhara H. Almuqrin ³

1.
Department of Basic Sciences, General Administration of Preparatory Year, King Faisal University, P.O. Box 400, Al Ahsa 31982, Saudi Arabia
2.
Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al Ahsa 31982, Saudi Arabia
3.
Department of Physics, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

Received: 24 March 2024 Revised: 27 May 2024 Accepted: 12 June 2024 Published: 24 June 2024
MSC : 34G20, 35A20, 35A22, 35R11

We focused on the analytical solution of strong nonlinearity and complicated time-fractional evolution equations, including the Sawada-Kotera equation, Ito equation, and Kaup-Kupershmidt equation, using an effective and accurate method known as the Aboodh residual power series method (ARPSM) in the framework of the Caputo operator. Therefore, the Caputo operator and the ARPSM are practical for figuring out a linear or nonlinear system with a fractional derivative. This technique was effectively proposed to obtain a set of analytical solutions for various types of fractional differential equations. The derived solutions enabled us to understand the mechanisms behind the propagation and generation of numerous nonlinear phenomena observed in diverse scientific domains, including plasma physics, fluid physics, and optical fibers. The fractional property also revealed some ambiguity that may be observed in many natural phenomena, and this is one of the most important distinguishing factors between fractional differential equations and non-fractional ones. We also helped clarify fractional calculus in nonlinear dynamics, motivating researchers to work in mathematical physics.
- fractional PDE,
- fractional Sawada-Kotera equation,
- fractional Ito equation,
- fractional Kaup-Kupershmidt equation,
- Aboodh residual power series method,
- Caputo operator,
- solitary waves
Citation: Humaira Yasmin, Aljawhara H. Almuqrin. Efficient solutions for time fractional Sawada-Kotera, Ito, and Kaup-Kupershmidt equations using an analytical technique[J]. AIMS Mathematics, 2024, 9(8): 20441-20466. doi: 10.3934/math.2024994

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Abstract

We focused on the analytical solution of strong nonlinearity and complicated time-fractional evolution equations, including the Sawada-Kotera equation, Ito equation, and Kaup-Kupershmidt equation, using an effective and accurate method known as the Aboodh residual power series method (ARPSM) in the framework of the Caputo operator. Therefore, the Caputo operator and the ARPSM are practical for figuring out a linear or nonlinear system with a fractional derivative. This technique was effectively proposed to obtain a set of analytical solutions for various types of fractional differential equations. The derived solutions enabled us to understand the mechanisms behind the propagation and generation of numerous nonlinear phenomena observed in diverse scientific domains, including plasma physics, fluid physics, and optical fibers. The fractional property also revealed some ambiguity that may be observed in many natural phenomena, and this is one of the most important distinguishing factors between fractional differential equations and non-fractional ones. We also helped clarify fractional calculus in nonlinear dynamics, motivating researchers to work in mathematical physics.

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