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Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations

In the present article, we related the analytical solution of the fractional-order dispersive partial differential equations, using the Laplace–Adomian decomposition method. The Caputo operator is used to define the derivative of fractional-order. Laplace–Adomian decomposition method solutions for b...

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Detalles Bibliográficos
Autores principales: Shah, Rasool, Khan, Hassan, Arif, Muhammad, Kumam, Poom
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514819/
https://www.ncbi.nlm.nih.gov/pubmed/33267049
http://dx.doi.org/10.3390/e21040335
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author Shah, Rasool
Khan, Hassan
Arif, Muhammad
Kumam, Poom
author_facet Shah, Rasool
Khan, Hassan
Arif, Muhammad
Kumam, Poom
author_sort Shah, Rasool
collection PubMed
description In the present article, we related the analytical solution of the fractional-order dispersive partial differential equations, using the Laplace–Adomian decomposition method. The Caputo operator is used to define the derivative of fractional-order. Laplace–Adomian decomposition method solutions for both fractional and integer orders are obtained in series form, showing higher convergence of the proposed method. Illustrative examples are considered to confirm the validity of the present method. The fractional order solutions that are convergent to integer order solutions are also investigated.
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spelling pubmed-75148192020-11-09 Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations Shah, Rasool Khan, Hassan Arif, Muhammad Kumam, Poom Entropy (Basel) Article In the present article, we related the analytical solution of the fractional-order dispersive partial differential equations, using the Laplace–Adomian decomposition method. The Caputo operator is used to define the derivative of fractional-order. Laplace–Adomian decomposition method solutions for both fractional and integer orders are obtained in series form, showing higher convergence of the proposed method. Illustrative examples are considered to confirm the validity of the present method. The fractional order solutions that are convergent to integer order solutions are also investigated. MDPI 2019-03-28 /pmc/articles/PMC7514819/ /pubmed/33267049 http://dx.doi.org/10.3390/e21040335 Text en © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Shah, Rasool
Khan, Hassan
Arif, Muhammad
Kumam, Poom
Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations
title Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations
title_full Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations
title_fullStr Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations
title_full_unstemmed Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations
title_short Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations
title_sort application of laplace–adomian decomposition method for the analytical solution of third-order dispersive fractional partial differential equations
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514819/
https://www.ncbi.nlm.nih.gov/pubmed/33267049
http://dx.doi.org/10.3390/e21040335
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