Fractional analysis of Benjamin-Bona-Mahony equation across natural transform iterative method: thermal engineering implementations
Abstract In this study, we apply the Natural Transform Iterative Method (NTIM), a relatively new and efficient analytical tool for solving fractional differential equations (FDEs). NTIM combines the Natural Transform and Daftardar-Jafari polynomials to construct approximate solutions without the nee...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-06-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-025-05720-8 |
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| author | Atia Nazneen Nasir Ali Syed M. Hussain Hijaz Ahmad Rashid Nawaz Laiq Zada Rida Irfan Kamel Guedri Abdulrazak H. Almaliki Mustafa Bayram |
| author_facet | Atia Nazneen Nasir Ali Syed M. Hussain Hijaz Ahmad Rashid Nawaz Laiq Zada Rida Irfan Kamel Guedri Abdulrazak H. Almaliki Mustafa Bayram |
| author_sort | Atia Nazneen |
| collection | DOAJ |
| description | Abstract In this study, we apply the Natural Transform Iterative Method (NTIM), a relatively new and efficient analytical tool for solving fractional differential equations (FDEs). NTIM combines the Natural Transform and Daftardar-Jafari polynomials to construct approximate solutions without the need for discretization, small parameters, or linearization. This method is particularly effective for handling fractional partial differential equations due to its simplicity and rapid convergence. In comparison with other established techniques, such as the Homotopy Perturbation Method (HPM), Adomian Decomposition Method (ADM), and Fractional Homotopy Analysis Transform Method (FHATM). NTIM demonstrates improved accuracy and computational efficiency. The method is validated through numerical and graphical comparisons with exact solutions, showing its potential for broader applications in nonlinear fractional systems. |
| format | Article |
| id | doaj-art-591043d787cb47d49efd3a2587f4a6ca |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-591043d787cb47d49efd3a2587f4a6ca2025-08-20T03:47:14ZengNature PortfolioScientific Reports2045-23222025-06-0115111410.1038/s41598-025-05720-8Fractional analysis of Benjamin-Bona-Mahony equation across natural transform iterative method: thermal engineering implementationsAtia Nazneen0Nasir Ali1Syed M. Hussain2Hijaz Ahmad3Rashid Nawaz4Laiq Zada5Rida Irfan6Kamel Guedri7Abdulrazak H. Almaliki8Mustafa Bayram9Department of Mathematics, Abdul Wali Khan University MardanDepartment of Mathematics, Abdul Wali Khan University MardanDepartment of Mathematics, Faculty of Science, Islamic University of MadinahDepartment of Mathematics, Faculty of Science, Islamic University of MadinahDepartment of Mathematics, Abdul Wali Khan University MardanDepartment of Mathematics, Abdul Wali Khan University MardanDepartment of Mathematics, COMSATS University Islamabad, Sahiwal CampusMechanical Engineering Department, College of Engineering and Architecture, Umm Al-Qura UniversityDepartment of Civil Engineering, College of Engineering, Taif UniversityDepartment of Computer Engineering, Biruni UniversityAbstract In this study, we apply the Natural Transform Iterative Method (NTIM), a relatively new and efficient analytical tool for solving fractional differential equations (FDEs). NTIM combines the Natural Transform and Daftardar-Jafari polynomials to construct approximate solutions without the need for discretization, small parameters, or linearization. This method is particularly effective for handling fractional partial differential equations due to its simplicity and rapid convergence. In comparison with other established techniques, such as the Homotopy Perturbation Method (HPM), Adomian Decomposition Method (ADM), and Fractional Homotopy Analysis Transform Method (FHATM). NTIM demonstrates improved accuracy and computational efficiency. The method is validated through numerical and graphical comparisons with exact solutions, showing its potential for broader applications in nonlinear fractional systems.https://doi.org/10.1038/s41598-025-05720-8Natural transform iterative method (NTIM)Thermal engineeringFractional order Benjamin-Bona-Mahony (FBBM) equationFBBM-Burger equation |
| spellingShingle | Atia Nazneen Nasir Ali Syed M. Hussain Hijaz Ahmad Rashid Nawaz Laiq Zada Rida Irfan Kamel Guedri Abdulrazak H. Almaliki Mustafa Bayram Fractional analysis of Benjamin-Bona-Mahony equation across natural transform iterative method: thermal engineering implementations Scientific Reports Natural transform iterative method (NTIM) Thermal engineering Fractional order Benjamin-Bona-Mahony (FBBM) equation FBBM-Burger equation |
| title | Fractional analysis of Benjamin-Bona-Mahony equation across natural transform iterative method: thermal engineering implementations |
| title_full | Fractional analysis of Benjamin-Bona-Mahony equation across natural transform iterative method: thermal engineering implementations |
| title_fullStr | Fractional analysis of Benjamin-Bona-Mahony equation across natural transform iterative method: thermal engineering implementations |
| title_full_unstemmed | Fractional analysis of Benjamin-Bona-Mahony equation across natural transform iterative method: thermal engineering implementations |
| title_short | Fractional analysis of Benjamin-Bona-Mahony equation across natural transform iterative method: thermal engineering implementations |
| title_sort | fractional analysis of benjamin bona mahony equation across natural transform iterative method thermal engineering implementations |
| topic | Natural transform iterative method (NTIM) Thermal engineering Fractional order Benjamin-Bona-Mahony (FBBM) equation FBBM-Burger equation |
| url | https://doi.org/10.1038/s41598-025-05720-8 |
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