Analytical Solutions of the Nonlinear Time-Fractional Coupled Boussinesq-Burger Equations Using Laplace Residual Power Series Technique

Sarhan, Aref; Burqan, Aliaa; Saadeh, Rania; Al–Zhour, Zeyad

doi:10.3390/fractalfract6110631

Cited by 16 publications

(3 citation statements)

References 51 publications

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“…Hosseini and Ansari had improved the equation stated in [26]. The finding was noticed by the authors using the modified kudryashov technique [27] and it was defined by Hoseini et al [28], using the exp-(−ψ(ζ))expansion methodology. Using the first integral technique, Yaslan and Girgin found the solution [29].…”

Section: Introductionmentioning

confidence: 96%

Analysis of chaotic structures, bifurcation and soliton solutions to fractional Boussinesq model

et al. 2023

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In this work, we used the space-time fractional coupled Boussinesq (STFCB) model that is essential tools in the study of quantum optics, steady physics, the variational string's acoustic waves, ion vibrational frequencies, hydro-magnetic waves in cold plasma and many other fields.~In order to put such new precise solutions of the aforementioned model, the modified Sardar-sub equation (MSSE) technique has been suggested with inside the sense of conformable derivative and the fractional order partial differential equation that is capable of changing into an ordinary differential equation by using the travelling wave transform.~The scoring of solitons and other solutions demonstrates the MSSE technique compatibility for different constant values, which are shown in 3-D, 2-D and contour plots.~Additionally, we discussed the examined model chaotic and dynamical tendencies.~The theory of plane dynamical system is used to examine the chaotic patterns of the systems.~The investigations are novel and unexamined.~They can be utilized to explain the physical phenomena which have been simulated to provide details on the brief dynamical characteristics.~According to numerical simulations modifying the parameters of frequencies and amplitudes has an impact on the system of dynamical properties. We indicated that the MSSE technique for creating precise solutions offers new and significant mathematical tools in applied mathematics.

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Section: Introductionmentioning

confidence: 96%

Analysis of chaotic structures, bifurcation and soliton solutions to fractional Boussinesq model

et al. 2023

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“…In addition, Kumar et al (2016) received the approximate solutions of time fractional coupled Boussinesq-Burger equations (TFCBBEs) by residual power series method. Sarhan et al (2022) obtained the series solutions of TFCBBEs using Laplace residual power series technique. Alrawashdeh and Bani-Issa (2021) achieved the approximate solutions by using fractional decomposition method to solve TFCBBEs.…”

Section: Introductionmentioning

confidence: 99%

“…(2016) received the approximate solutions of time fractional coupled Boussinesq-Burger equations (TFCBBEs) by residual power series method. Sarhan et al. (2022) obtained the series solutions of TFCBBEs using Laplace residual power series technique.…”

Section: Introductionmentioning

confidence: 99%

Application of Laplace Adomian decomposition method for fractional Fokker-Planck equation and time fractional coupled Boussinesq-Burger equations

Zhang,

Wang

2024

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PurposeFractional Fokker-Planck equation (FFPE) and time fractional coupled Boussinesq-Burger equations (TFCBBEs) play important roles in the fields of solute transport, fluid dynamics, respectively. Although there are many methods for solving the approximate solution, simple and effective methods are more preferred. This paper aims to utilize Laplace Adomian decomposition method (LADM) to construct approximate solutions for these two types of equations and gives some examples of numerical calculations, which can prove the validity of LADM by comparing the error between the calculated results and the exact solution.Design/methodology/approachThis paper analyzes and investigates the time-space fractional partial differential equations based on the LADM method in the sense of Caputo fractional derivative, which is a combination of the Laplace transform and the Adomian decomposition method. LADM method was first proposed by Khuri in 2001. Many partial differential equations which can describe the physical phenomena are solved by applying LADM and it has been used extensively to solve approximate solutions of partial differential and fractional partial differential equations.FindingsThis paper obtained an approximate solution to the FFPE and TFCBBEs by using the LADM. A number of numerical examples and graphs are used to compare the errors between the results and the exact solutions. The results show that LADM is a simple and effective mathematical technique to construct the approximate solutions of nonlinear time-space fractional equations in this work.Originality/valueThis paper verifies the effectiveness of this method by using the LADM to solve the FFPE and TFCBBEs. In addition, these two equations are very meaningful, and this paper will be helpful in the study of atmospheric diffusion, shallow water waves and other areas. And this paper also generalizes the drift and diffusion terms of the FFPE equation to the general form, which provides a great convenience for our future studies.

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Numerical investigation of a fractional model of a tumor-immune surveillance via Caputo operator

Alshammari,

Alabedalhadi

et al. 2024

Alexandria Engineering Journal

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Analytical Solutions of the Nonlinear Time-Fractional Coupled Boussinesq-Burger Equations Using Laplace Residual Power Series Technique

Cited by 16 publications

References 51 publications

Analysis of chaotic structures, bifurcation and soliton solutions to fractional Boussinesq model

Analysis of chaotic structures, bifurcation and soliton solutions to fractional Boussinesq model

Application of Laplace Adomian decomposition method for fractional Fokker-Planck equation and time fractional coupled Boussinesq-Burger equations

Numerical investigation of a fractional model of a tumor-immune surveillance via Caputo operator

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