<abstract xmlns="http://www.w3.org/1999/xhtml">

In this work, a coupled system of time-fractional modified Burgers’ equations is considered. Three different fractional operators: Caputo, Caputo-Fabrizio and Atangana-Baleanu operators are implemented for the equations. Also, two different scenarios are examined for each fractional operator: when the initial conditions are u(x, y, 0) = sin(xy), v(x, y, 0) = sin(xy), and when they are u(x, y, 0) = e{−kxy}, v(x, y, 0) = e{−kxy}, where k, α are some positive constants. With the aid of computable Adomian polynomials, the solutions are obtained using Laplace Adomian decomposition method (LADM). The method does not need linearization, weak nonlinearity assumptions or perturbation theory. Simulations are also presented to support theoretical results, and the behaviour of the solutions under the three different fractional operators compared.
</abstract>

In this work, a coupled system of time-fractional modified Burgers’ equations is considered. Three different fractional operators: Caputo, Caputo-Fabrizio and Atangana-Baleanu operators are implemented for the equations. Also, two different scenarios are examined for each fractional operator: when the initial conditions are u(x, y, 0) = sin(xy), v(x, y, 0) = sin(xy), and when they are u(x, y, 0) = e{−kxy}, v(x, y, 0) = e{−kxy}, where k, α are some positive constants. With the aid of computable Adomian polynomials, the solutions are obtained using Laplace Adomian decomposition method (LADM). The method does not need linearization, weak nonlinearity assumptions or perturbation theory. Simulations are also presented to support theoretical results, and the behaviour of the solutions under the three different fractional operators compared.

Solution of the Modified Time Fractional Coupled Burgers Equations Using Laplace Adomian Decompostion Method

Acta Mechanica et Automatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this work, a coupled system of time-fractional modified Burgers’ equations is considered. Three different fractional operators: Caputo, Caputo-Fabrizio and...

Solution of the Modified Time Fractional Coupled Burgers Equations Using Laplace Adomian Decompostion Method

Publié en ligne: 15 févr. 2023

Pages: 124 - 132

Reçu: 25 sept. 2022

Accepté: 01 nov. 2022

DOI: https://doi.org/10.2478/ama-2023-0014

Mots clés
Burgers equations, Fractional derivatives, Laplace Adomian decomposition method, Semi-analytic solutions, Simulations

© 2023 Andrew Omame et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Solution of the Modified Time Fractional Coupled Burgers Equations Using Laplace Adomian Decompostion Method

Publié en ligne: 15 févr. 2023

Pages: 124 - 132

Reçu: 25 sept. 2022

Accepté: 01 nov. 2022

DOI: https://doi.org/10.2478/ama-2023-0014

Mots clésBurgers equations, Fractional derivatives, Laplace Adomian decomposition method, Semi-analytic solutions, Simulations

© 2023 Andrew Omame et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
Burgers equations, Fractional derivatives, Laplace Adomian decomposition method, Semi-analytic solutions, Simulations