A new application of conformable Laplace decomposition method for fractional Newell-Whitehead-Segel equation

Muammer Ayata; Ozan Özkan; Muammer Ayata; Ozan Özkan

doi:10.3934/math.2020474

AIMS Mathematics

2020, Volume 5, Issue 6: 7402-7412. doi: 10.3934/math.2020474

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Research article

A new application of conformable Laplace decomposition method for fractional Newell-Whitehead-Segel equation

Muammer Ayata ^,,
Ozan Özkan

Department of Mathematics, Faculty of Science, Selcuk University, Konya, 42003, Turkey

Received: 26 June 2020 Accepted: 06 September 2020 Published: 21 September 2020
MSC : 26A33, 34A08, 35R11

In this study, it is the first time that conformable Laplace decomposition method (CLDM) is applied to fractional Newell-Whitehead-Segel (NWS) equation which is one of the most significant amplitude equations in physics. The method consists of the unification of conformable Laplace transform and Adomian decomposition method (ADM) and it is used for finding approximate analytical solutions of linear-nonlinear fractional PDE's. The results show that this CLDM is quite powerful in solving fractional PDE's.
- Conformable fractional derivative,
- Conformable differential equations,
- Newell-Whitehead-Segel equation,
- Amplitude equations,
- Laplace transform,
- Adomian decomposition method
Citation: Muammer Ayata, Ozan Özkan. A new application of conformable Laplace decomposition method for fractional Newell-Whitehead-Segel equation[J]. AIMS Mathematics, 2020, 5(6): 7402-7412. doi: 10.3934/math.2020474

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Abstract

In this study, it is the first time that conformable Laplace decomposition method (CLDM) is applied to fractional Newell-Whitehead-Segel (NWS) equation which is one of the most significant amplitude equations in physics. The method consists of the unification of conformable Laplace transform and Adomian decomposition method (ADM) and it is used for finding approximate analytical solutions of linear-nonlinear fractional PDE's. The results show that this CLDM is quite powerful in solving fractional PDE's.

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