The Aboodh transformation-based homotopy perturbation method: new hope for fractional calculus
Fractional differential equations can model various complex problems in physics and engineering, but there is no universal method to solve fractional models precisely. This paper offers a new hope for this purpose by coupling the homotopy perturbation method with Aboodh transform. The new hybrid tec...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2023-04-01
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| Series: | Frontiers in Physics |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2023.1168795/full |
| _version_ | 1797834934506749952 |
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| author | Huiqiang Tao Naveed Anjum Yong-Ju Yang |
| author_facet | Huiqiang Tao Naveed Anjum Yong-Ju Yang |
| author_sort | Huiqiang Tao |
| collection | DOAJ |
| description | Fractional differential equations can model various complex problems in physics and engineering, but there is no universal method to solve fractional models precisely. This paper offers a new hope for this purpose by coupling the homotopy perturbation method with Aboodh transform. The new hybrid technique leads to a simple approach to finding an approximate solution, which converges fast to the exact one with less computing effort. An example of the fractional casting-mold system is given to elucidate the hope for fractional calculus, and this paper serves as a model for other fractional differential equations. |
| first_indexed | 2024-04-09T14:45:28Z |
| format | Article |
| id | doaj.art-457c0165a6654ad18d4431de8595064f |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-04-09T14:45:28Z |
| publishDate | 2023-04-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-457c0165a6654ad18d4431de8595064f2023-05-02T15:57:59ZengFrontiers Media S.A.Frontiers in Physics2296-424X2023-04-011110.3389/fphy.2023.11687951168795The Aboodh transformation-based homotopy perturbation method: new hope for fractional calculusHuiqiang Tao0Naveed Anjum1Yong-Ju Yang2School of Mathematics and Statistics, Huanghuai University, Zhumadian, ChinaDepartment of Mathematics, Government College University, Faisalabad, PakistanSchool of Mathematics and Statistics, Nanyang Normal University, Nanyang, ChinaFractional differential equations can model various complex problems in physics and engineering, but there is no universal method to solve fractional models precisely. This paper offers a new hope for this purpose by coupling the homotopy perturbation method with Aboodh transform. The new hybrid technique leads to a simple approach to finding an approximate solution, which converges fast to the exact one with less computing effort. An example of the fractional casting-mold system is given to elucidate the hope for fractional calculus, and this paper serves as a model for other fractional differential equations.https://www.frontiersin.org/articles/10.3389/fphy.2023.1168795/fullhomotopy perturbation methodAboodh transformHe’s polynomialsfractional differential equationtwo-scale fractal theory |
| spellingShingle | Huiqiang Tao Naveed Anjum Yong-Ju Yang The Aboodh transformation-based homotopy perturbation method: new hope for fractional calculus Frontiers in Physics homotopy perturbation method Aboodh transform He’s polynomials fractional differential equation two-scale fractal theory |
| title | The Aboodh transformation-based homotopy perturbation method: new hope for fractional calculus |
| title_full | The Aboodh transformation-based homotopy perturbation method: new hope for fractional calculus |
| title_fullStr | The Aboodh transformation-based homotopy perturbation method: new hope for fractional calculus |
| title_full_unstemmed | The Aboodh transformation-based homotopy perturbation method: new hope for fractional calculus |
| title_short | The Aboodh transformation-based homotopy perturbation method: new hope for fractional calculus |
| title_sort | aboodh transformation based homotopy perturbation method new hope for fractional calculus |
| topic | homotopy perturbation method Aboodh transform He’s polynomials fractional differential equation two-scale fractal theory |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2023.1168795/full |
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