The analytical analysis of nonlinear fractional-order dynamical models

Jiabin Xu; Hassan Khan; Rasool Shah; A.A. Alderremy; Shaban Aly; Dumitru Baleanu; Jiabin Xu; Hassan Khan; Rasool Shah; A.A. Alderremy; Shaban Aly; Dumitru Baleanu

doi:10.3934/math.2021364

AIMS Mathematics

2021, Volume 6, Issue 6: 6201-6219. doi: 10.3934/math.2021364

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Research article Special Issues

The analytical analysis of nonlinear fractional-order dynamical models

1.
School of Mathematics and Information Sciences, Neijiang Normal University, 641112, Sichuan Province, China
2.
Department of Mathematics Abdul Wali Khan University Mardan (AWKUM), Pakistan
3.
Department of Mathematics, Near East University TRNC, Mersin 10, Turkey
4.
Department of Mathematics, Faculty of Science, King Khalid University, Abha 61413, Kingdom of Saudi Arabia
5.
Department of Mathematics, Faculty of Science, AL-Azhar University, Assiut, 71516, Egypt
6.
Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
7.
Institute of Space Sciences, Magurele-Bucharest, Romania

Received: 12 November 2020 Accepted: 09 March 2021 Published: 08 April 2021
MSC : 34A34, 35A20, 35A22, 44A10, 33B15

The present research paper is related to the analytical solution of fractional-order nonlinear Swift-Hohenberg equations using an efficient technique. The presented model is related to the temperature and thermal convection of fluid dynamics which can also be used to explain the formation process in liquid surfaces bounded along a horizontally well-conducting boundary. In this work Laplace Adomian decomposition method is implemented because it require small volume of calculations. Unlike the variational iteration method and Homotopy pertubation method, the suggested technique required no variational parameter and having simple calculation of fractional derivative respectively. Numerical examples verify the validity of the suggested method. It is confirmed that the present method's solutions are in close contact with the solutions of other existing methods. It is also investigated through graphs and tables that the suggested method's solutions are almost identical with different analytical methods.
- Laplace transform,
- Adomian decomposition method,
- Swift-Hohenberg equation,
- Caputo operator
Citation: Jiabin Xu, Hassan Khan, Rasool Shah, A.A. Alderremy, Shaban Aly, Dumitru Baleanu. The analytical analysis of nonlinear fractional-order dynamical models[J]. AIMS Mathematics, 2021, 6(6): 6201-6219. doi: 10.3934/math.2021364

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Abstract

The present research paper is related to the analytical solution of fractional-order nonlinear Swift-Hohenberg equations using an efficient technique. The presented model is related to the temperature and thermal convection of fluid dynamics which can also be used to explain the formation process in liquid surfaces bounded along a horizontally well-conducting boundary. In this work Laplace Adomian decomposition method is implemented because it require small volume of calculations. Unlike the variational iteration method and Homotopy pertubation method, the suggested technique required no variational parameter and having simple calculation of fractional derivative respectively. Numerical examples verify the validity of the suggested method. It is confirmed that the present method's solutions are in close contact with the solutions of other existing methods. It is also investigated through graphs and tables that the suggested method's solutions are almost identical with different analytical methods.

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