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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Main Authors: Atia Nazneen, Nasir Ali, Syed M. Hussain, Hijaz Ahmad, Rashid Nawaz, Laiq Zada, Rida Irfan, Kamel Guedri, Abdulrazak H. Almaliki, Mustafa Bayram
Format: Article
Language:English
Published: Nature Portfolio 2025-06-01
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
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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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