<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Many investigations related to the analytical solutions of the nonlinear sub-diffusion equation exist. In this paper, we investigate the conditions under which the analytical and the approximate solutions of the nonlinear sub-diffusion equation and the nonlinear sub-advection dispersion equation exist. In other words, the problems of existence and uniqueness of the solutions the fractional diffusion equations have been addressed. We use the Banach fixed Theorem. After proving the existence and uniqueness, we propose the analytical and the approximate solutions of the nonlinear sub-diffusion, and the nonlinear sub-advection dispersion equations. We analyze the impact of the sub-diffusion coefficient, the advection coefficient and the dispersion coefficient in the diffusion processes. The homotopy perturbation Laplace transform method has been used in this paper. Some numerical examples are provided to illustrate the main results of the article.</p></abstract>

Many investigations related to the analytical solutions of the nonlinear sub-diffusion equation exist. In this paper, we investigate the conditions under which the analytical and the approximate solutions of the nonlinear sub-diffusion equation and the nonlinear sub-advection dispersion equation exist. In other words, the problems of existence and uniqueness of the solutions the fractional diffusion equations have been addressed. We use the Banach fixed Theorem. After proving the existence and uniqueness, we propose the analytical and the approximate solutions of the nonlinear sub-diffusion, and the nonlinear sub-advection dispersion equations. We analyze the impact of the sub-diffusion coefficient, the advection coefficient and the dispersion coefficient in the diffusion processes. The homotopy perturbation Laplace transform method has been used in this paper. Some numerical examples are provided to illustrate the main results of the article.

Nonlinear sub-diffusion and nonlinear sub-diffusion dispersion equations and their proposed solutions

Département de Mathématiques de la Décision

Université Cheikh Anta Diop de Dakar, Faculté des Sciences Economiques et Gestion

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

Many investigations related to the analytical solutions of the nonlinear sub-diffusion equation exist. In this paper, we investigate the conditions under which...

Nonlinear sub-diffusion and nonlinear sub-diffusion dispersion equations and their proposed solutions

Published Online: Mar 31, 2020

Page range: 221 - 236

Received: May 28, 2019

Accepted: Jul 10, 2019

DOI: https://doi.org/10.2478/amns.2020.1.00020

Keywords
Nonlinear sub-advection dispersion equation, the nonlinear sub-diffusion equation, Approximate solution

© 2020 Ndolane Sene, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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Nonlinear sub-diffusion and nonlinear sub-diffusion dispersion equations and their proposed solutions

Published Online: Mar 31, 2020

Page range: 221 - 236

Received: May 28, 2019

Accepted: Jul 10, 2019

DOI: https://doi.org/10.2478/amns.2020.1.00020

KeywordsNonlinear sub-advection dispersion equation, the nonlinear sub-diffusion equation, Approximate solution

© 2020 Ndolane Sene, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Keywords
Nonlinear sub-advection dispersion equation, the nonlinear sub-diffusion equation, Approximate solution