A new study on the Newell-Whitehead-Segel equation with Caputo-Fabrizio fractional derivative

Aslı Alkan; Halil Anaç; Aslı Alkan; Halil Anaç

doi:10.3934/math.20241358

AIMS Mathematics

2024, Volume 9, Issue 10: 27979-27997. doi: 10.3934/math.20241358

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A new study on the Newell-Whitehead-Segel equation with Caputo-Fabrizio fractional derivative

Aslı Alkan ^{1
,
,},
Halil Anaç ²

1.
Department of Mathematics, Faculty of Science, Fırat University, Elazığ 23119, Turkey
2.
Department of Computer Technologies, Torul Vocational School, Gumushane University, Gumushane 29802, Turkey

Received: 12 May 2024 Revised: 15 July 2024 Accepted: 02 August 2024 Published: 27 September 2024
MSC : 35C05, 35R11, 65R10

In this research, we propose a new numerical method that combines with the Caputo-Fabrizio Elzaki transform and the q-homotopy analysis transform method. This work aims to analyze the Caputo-Fabrizio fractional Newell-Whitehead-Segel (NWS) equation utilizing the Caputo-Fabrizio q-Elzaki homotopy analysis transform method. The Newell-Whitehead-Segel equation is a partial differential equation employed for modeling the dynamics of reaction-diffusion systems, specifically in the realm of pattern generation in biological and chemical systems. A convergence analysis of the proposed method was performed. Two-dimensional and three-dimensional graphs of the solutions have been drawn with the Maple software. It is seen that the resulting proposed method is more powerful and effective than the Aboodh transform homotopy perturbation method and conformable Laplace decomposition method in the results.
Citation: Aslı Alkan, Halil Anaç. A new study on the Newell-Whitehead-Segel equation with Caputo-Fabrizio fractional derivative[J]. AIMS Mathematics, 2024, 9(10): 27979-27997. doi: 10.3934/math.20241358

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Abstract

In this research, we propose a new numerical method that combines with the Caputo-Fabrizio Elzaki transform and the q-homotopy analysis transform method. This work aims to analyze the Caputo-Fabrizio fractional Newell-Whitehead-Segel (NWS) equation utilizing the Caputo-Fabrizio q-Elzaki homotopy analysis transform method. The Newell-Whitehead-Segel equation is a partial differential equation employed for modeling the dynamics of reaction-diffusion systems, specifically in the realm of pattern generation in biological and chemical systems. A convergence analysis of the proposed method was performed. Two-dimensional and three-dimensional graphs of the solutions have been drawn with the Maple software. It is seen that the resulting proposed method is more powerful and effective than the Aboodh transform homotopy perturbation method and conformable Laplace decomposition method in the results.

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