Analytical Solutions of Time-Fractional Navier–Stokes Equations Employing Homotopy Perturbation–Laplace Transform Method
The aim of this article is to introduce analytical and approximate techniques to obtain the solution of time-fractional Navier–Stokes equations. This proposed technique consists is coupling the homotopy perturbation method (HPM) and Laplace transform (LT). The time-fractional derivative used is the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-12-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/1/23 |
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| author | Awatif Muflih Alqahtani Hamza Mihoubi Yacine Arioua Brahim Bouderah |
| author_facet | Awatif Muflih Alqahtani Hamza Mihoubi Yacine Arioua Brahim Bouderah |
| author_sort | Awatif Muflih Alqahtani |
| collection | DOAJ |
| description | The aim of this article is to introduce analytical and approximate techniques to obtain the solution of time-fractional Navier–Stokes equations. This proposed technique consists is coupling the homotopy perturbation method (HPM) and Laplace transform (LT). The time-fractional derivative used is the Caputo–Hadamard fractional derivative (CHFD). The effectiveness of this method is demonstrated and validated through two test problems. The results show that the proposed method is robust, efficient, and easy to implement for both linear and nonlinear problems in science and engineering. Additionally, its computational efficiency requires less computation compared to other schemes. |
| format | Article |
| id | doaj-art-988b95403dd64d5b9ec220724fcc0975 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-988b95403dd64d5b9ec220724fcc09752025-01-24T13:33:24ZengMDPI AGFractal and Fractional2504-31102024-12-01912310.3390/fractalfract9010023Analytical Solutions of Time-Fractional Navier–Stokes Equations Employing Homotopy Perturbation–Laplace Transform MethodAwatif Muflih Alqahtani0Hamza Mihoubi1Yacine Arioua2Brahim Bouderah3Department of Mathematics, Shaqra University, Riyadh 11972, Saudi ArabiaDepartment of Mathematics, University of M’sila, University Pole, Road Bordj Bou Arreridj, M’sila 28000, AlgeriaDepartment of Mathematics, University of M’sila, University Pole, Road Bordj Bou Arreridj, M’sila 28000, AlgeriaDepartment of Mathematics, University of M’sila, University Pole, Road Bordj Bou Arreridj, M’sila 28000, AlgeriaThe aim of this article is to introduce analytical and approximate techniques to obtain the solution of time-fractional Navier–Stokes equations. This proposed technique consists is coupling the homotopy perturbation method (HPM) and Laplace transform (LT). The time-fractional derivative used is the Caputo–Hadamard fractional derivative (CHFD). The effectiveness of this method is demonstrated and validated through two test problems. The results show that the proposed method is robust, efficient, and easy to implement for both linear and nonlinear problems in science and engineering. Additionally, its computational efficiency requires less computation compared to other schemes.https://www.mdpi.com/2504-3110/9/1/23fractional Navier–Stokes equationCaputo–Hadamard fractional derivativehomotopy perturbation–Laplace transform method |
| spellingShingle | Awatif Muflih Alqahtani Hamza Mihoubi Yacine Arioua Brahim Bouderah Analytical Solutions of Time-Fractional Navier–Stokes Equations Employing Homotopy Perturbation–Laplace Transform Method Fractal and Fractional fractional Navier–Stokes equation Caputo–Hadamard fractional derivative homotopy perturbation–Laplace transform method |
| title | Analytical Solutions of Time-Fractional Navier–Stokes Equations Employing Homotopy Perturbation–Laplace Transform Method |
| title_full | Analytical Solutions of Time-Fractional Navier–Stokes Equations Employing Homotopy Perturbation–Laplace Transform Method |
| title_fullStr | Analytical Solutions of Time-Fractional Navier–Stokes Equations Employing Homotopy Perturbation–Laplace Transform Method |
| title_full_unstemmed | Analytical Solutions of Time-Fractional Navier–Stokes Equations Employing Homotopy Perturbation–Laplace Transform Method |
| title_short | Analytical Solutions of Time-Fractional Navier–Stokes Equations Employing Homotopy Perturbation–Laplace Transform Method |
| title_sort | analytical solutions of time fractional navier stokes equations employing homotopy perturbation laplace transform method |
| topic | fractional Navier–Stokes equation Caputo–Hadamard fractional derivative homotopy perturbation–Laplace transform method |
| url | https://www.mdpi.com/2504-3110/9/1/23 |
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