The analytical analysis of nonlinear fractional-order dynamical models
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...
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-04-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2021364?viewType=HTML |
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| author | Jiabin Xu Hassan Khan Rasool Shah A.A. Alderremy Shaban Aly Dumitru Baleanu |
| author_facet | Jiabin Xu Hassan Khan Rasool Shah A.A. Alderremy Shaban Aly Dumitru Baleanu |
| author_sort | Jiabin Xu |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-17T19:50:48Z |
| format | Article |
| id | doaj.art-1708399d4fd14fd8ab507f92b5080cd4 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-17T19:50:48Z |
| publishDate | 2021-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-1708399d4fd14fd8ab507f92b5080cd42022-12-21T21:34:44ZengAIMS PressAIMS Mathematics2473-69882021-04-01666201621910.3934/math.2021364The analytical analysis of nonlinear fractional-order dynamical modelsJiabin Xu0Hassan Khan1Rasool Shah2A.A. Alderremy3Shaban Aly4Dumitru Baleanu51. School of Mathematics and Information Sciences, Neijiang Normal University, 641112, Sichuan Province, China2. Department of Mathematics Abdul Wali Khan University Mardan (AWKUM), Pakistan 3. Department of Mathematics, Near East University TRNC, Mersin 10, Turkey2. Department of Mathematics Abdul Wali Khan University Mardan (AWKUM), Pakistan4. Department of Mathematics, Faculty of Science, King Khalid University, Abha 61413, Kingdom of Saudi Arabia4. 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, Egypt6. Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey 7. Institute of Space Sciences, Magurele-Bucharest, RomaniaThe 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.https://www.aimspress.com/article/doi/10.3934/math.2021364?viewType=HTMLlaplace transformadomian decomposition methodswift-hohenberg equationcaputo operator |
| spellingShingle | Jiabin Xu Hassan Khan Rasool Shah A.A. Alderremy Shaban Aly Dumitru Baleanu The analytical analysis of nonlinear fractional-order dynamical models AIMS Mathematics laplace transform adomian decomposition method swift-hohenberg equation caputo operator |
| title | The analytical analysis of nonlinear fractional-order dynamical models |
| title_full | The analytical analysis of nonlinear fractional-order dynamical models |
| title_fullStr | The analytical analysis of nonlinear fractional-order dynamical models |
| title_full_unstemmed | The analytical analysis of nonlinear fractional-order dynamical models |
| title_short | The analytical analysis of nonlinear fractional-order dynamical models |
| title_sort | analytical analysis of nonlinear fractional order dynamical models |
| topic | laplace transform adomian decomposition method swift-hohenberg equation caputo operator |
| url | https://www.aimspress.com/article/doi/10.3934/math.2021364?viewType=HTML |
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