An attractive approach associated with transform functions for solving certain fractional Swift-Hohenberg equation
type: Item
instance of: scholarly article
title: An attractive approach associated with transform functions for solving certain fractional Swift-Hohenberg equation
zbMATH Open document ID: 1479.35909
DOI: 10.1155/2021/3230272
author: Mohammad Alaroud
author: Nedal Tahat
author: D. L. Suthar
author: Selma Gulyaz-Ozyurt
author: S. K. Q. Al-Omari
published in: Journal of Function Spaces
publication date: 2021-12-16T00:00:00Z
review text: Summary: 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 \(\beta\) 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.
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35K30
Mathematics Subject Classification ID: 35K58
zbMATH DE Number: 7446721
zbMATH Keywords: Laplace residual power series (LRPS) technique
zbMATH Keywords: time-Caputo fractional derivatives
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/3230272
OpenAlex ID: W3212572808
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description: scientific article; zbMATH DE number 7446721