An Attractive Approach Associated with Transform Functions for Solving Certain Fractional Swift-Hohenberg Equation

Many phenomena in physics and engineering can be built by linear and nonlinear fractional partial differential equations which are considered an accurate instrument to interpret these phenomena. In the current manuscript, the approximate analytical solutions for linear and nonlinear time-fractional...

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Autores principales:	Mohammad Alaroud, Nedal Tahat, Shrideh Al-Omari, D. L. Suthar, Selma Gulyaz-Ozyurt
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/be90d3794bed45e89f547cda84571cfe
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spelling	oai:doaj.org-article:be90d3794bed45e89f547cda84571cfe2021-11-22T01:09:29ZAn Attractive Approach Associated with Transform Functions for Solving Certain Fractional Swift-Hohenberg Equation2314-888810.1155/2021/3230272https://doaj.org/article/be90d3794bed45e89f547cda84571cfe2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/3230272https://doaj.org/toc/2314-8888Many phenomena in physics and engineering can be built by linear and nonlinear fractional partial differential equations which are considered an accurate instrument to interpret these phenomena. In the current manuscript, the approximate analytical solutions for linear and nonlinear time-fractional Swift-Hohenberg equations are created and studied by means of a recent superb technique, named the Laplace residual power series (LRPS) technique under the time-Caputo fractional derivatives. The proposed technique is a combination of the generalized Taylor’s formula and the Laplace transform operator, which depends mainly on the concept of limit at infinity to find the unknown functions for the fractional series expansions in the Laplace space with fewer computations and more accuracy comparing with the classical RPS that depends on the Caputo fractional derivative for each step in obtaining the coefficient expansion. To test the simplicity, performance, and applicability of the present method, three numerical problems of the time-fractional Swift-Hohenberg initial value problems are considered. The impact of the fractional order β on the behavior of the approximate solutions at fixed bifurcation parameter is shown graphically and numerically. Obtained results emphasized that the LRPS technique is an easy, efficient, and speed approach for the exact description of the linear and nonlinear time-fractional models that arise in natural sciences.Mohammad AlaroudNedal TahatShrideh Al-OmariD. L. SutharSelma Gulyaz-OzyurtHindawi LimitedarticleMathematicsQA1-939ENJournal of Function Spaces, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Mohammad Alaroud Nedal Tahat Shrideh Al-Omari D. L. Suthar Selma Gulyaz-Ozyurt An Attractive Approach Associated with Transform Functions for Solving Certain Fractional Swift-Hohenberg Equation
description	Many phenomena in physics and engineering can be built by linear and nonlinear fractional partial differential equations which are considered an accurate instrument to interpret these phenomena. In the current manuscript, the approximate analytical solutions for linear and nonlinear time-fractional Swift-Hohenberg equations are created and studied by means of a recent superb technique, named the Laplace residual power series (LRPS) technique under the time-Caputo fractional derivatives. The proposed technique is a combination of the generalized Taylor’s formula and the Laplace transform operator, which depends mainly on the concept of limit at infinity to find the unknown functions for the fractional series expansions in the Laplace space with fewer computations and more accuracy comparing with the classical RPS that depends on the Caputo fractional derivative for each step in obtaining the coefficient expansion. To test the simplicity, performance, and applicability of the present method, three numerical problems of the time-fractional Swift-Hohenberg initial value problems are considered. The impact of the fractional order β on the behavior of the approximate solutions at fixed bifurcation parameter is shown graphically and numerically. Obtained results emphasized that the LRPS technique is an easy, efficient, and speed approach for the exact description of the linear and nonlinear time-fractional models that arise in natural sciences.
format	article
author	Mohammad Alaroud Nedal Tahat Shrideh Al-Omari D. L. Suthar Selma Gulyaz-Ozyurt
author_facet	Mohammad Alaroud Nedal Tahat Shrideh Al-Omari D. L. Suthar Selma Gulyaz-Ozyurt
author_sort	Mohammad Alaroud
title	An Attractive Approach Associated with Transform Functions for Solving Certain Fractional Swift-Hohenberg Equation
title_short	An Attractive Approach Associated with Transform Functions for Solving Certain Fractional Swift-Hohenberg Equation
title_full	An Attractive Approach Associated with Transform Functions for Solving Certain Fractional Swift-Hohenberg Equation
title_fullStr	An Attractive Approach Associated with Transform Functions for Solving Certain Fractional Swift-Hohenberg Equation
title_full_unstemmed	An Attractive Approach Associated with Transform Functions for Solving Certain Fractional Swift-Hohenberg Equation
title_sort	attractive approach associated with transform functions for solving certain fractional swift-hohenberg equation
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/be90d3794bed45e89f547cda84571cfe
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An Attractive Approach Associated with Transform Functions for Solving Certain Fractional Swift-Hohenberg Equation

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