Stellar structure via truncated M-fractional Lane–Emden solutions

Abstract The Lane–Emden equation (LEE) is essential for modeling the structure of self-gravitating, spherically symmetric polytropic stars in hydrostatic equilibrium. Astronomy commonly employs it to depict normal stars, white dwarfs, and other celestial systems. This paper presents a new formulatio...

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Main Authors: Mohamed I. Nouh, Emad A.-B. Abdel-Salam, Abaker A. Hassaballa, A. M. Awad, M. S. Jazmati, M. S. M. Bahgat
Format: Article
Language:English
Published: Nature Portfolio 2025-04-01
Series:Scientific Reports
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Online Access:https://doi.org/10.1038/s41598-025-96734-9
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author Mohamed I. Nouh
Emad A.-B. Abdel-Salam
Abaker A. Hassaballa
A. M. Awad
M. S. Jazmati
M. S. M. Bahgat
author_facet Mohamed I. Nouh
Emad A.-B. Abdel-Salam
Abaker A. Hassaballa
A. M. Awad
M. S. Jazmati
M. S. M. Bahgat
author_sort Mohamed I. Nouh
collection DOAJ
description Abstract The Lane–Emden equation (LEE) is essential for modeling the structure of self-gravitating, spherically symmetric polytropic stars in hydrostatic equilibrium. Astronomy commonly employs it to depict normal stars, white dwarfs, and other celestial systems. This paper presents a new formulation of the LEE using truncated M-fractional derivatives (TMD), providing a fractional generalization that expands the conventional comprehension of polytropic gas spheres. Using the accelerated power series approach, we find solutions to the TMD Lane–Emden equation and create polytropic models spanning a variety of polytropic indices. Our results give fundamental insights into stellar properties: whereas the initial zero of the fractional Lane–Emden function grows with decreasing fractional parameters, the radius and mass of polytropic models representing stars like the Sun and white dwarfs decrease under the same circumstances. This mismatch underlines the importance of fractional factors on the structural scaling of stars, offering a broader insight into their physical features. The fractional polytropic models presented here expand the classic theory of polytropes and provide possible applications in comprehending the complex behavior of varied astrophysical phenomena under fractional calculus frameworks.
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spelling doaj-art-4a83b9919db44f7fbcae97ce30725f872025-08-20T03:06:57ZengNature PortfolioScientific Reports2045-23222025-04-0115111710.1038/s41598-025-96734-9Stellar structure via truncated M-fractional Lane–Emden solutionsMohamed I. Nouh0Emad A.-B. Abdel-Salam1Abaker A. Hassaballa2A. M. Awad3M. S. Jazmati4M. S. M. Bahgat5Astronomy Department, National Research Institute of Astronomy and GeophysicsDepartment of Mathematics, Faculty of Science, New Valley UniversityCenter for Scientific Research and Entrepreneurship, Northern Border UniversityDepartment of Mathematics, Faculty of Science, New Valley UniversityDepartment of Mathematics, College of Science, Qassim UniversityDepartment of Mathematics, College of Science, Qassim UniversityAbstract The Lane–Emden equation (LEE) is essential for modeling the structure of self-gravitating, spherically symmetric polytropic stars in hydrostatic equilibrium. Astronomy commonly employs it to depict normal stars, white dwarfs, and other celestial systems. This paper presents a new formulation of the LEE using truncated M-fractional derivatives (TMD), providing a fractional generalization that expands the conventional comprehension of polytropic gas spheres. Using the accelerated power series approach, we find solutions to the TMD Lane–Emden equation and create polytropic models spanning a variety of polytropic indices. Our results give fundamental insights into stellar properties: whereas the initial zero of the fractional Lane–Emden function grows with decreasing fractional parameters, the radius and mass of polytropic models representing stars like the Sun and white dwarfs decrease under the same circumstances. This mismatch underlines the importance of fractional factors on the structural scaling of stars, offering a broader insight into their physical features. The fractional polytropic models presented here expand the classic theory of polytropes and provide possible applications in comprehending the complex behavior of varied astrophysical phenomena under fractional calculus frameworks.https://doi.org/10.1038/s41598-025-96734-9Polytropic gas sphereLane–Emden equationTruncated M-fractional derivativeWhite dwarfs
spellingShingle Mohamed I. Nouh
Emad A.-B. Abdel-Salam
Abaker A. Hassaballa
A. M. Awad
M. S. Jazmati
M. S. M. Bahgat
Stellar structure via truncated M-fractional Lane–Emden solutions
Scientific Reports
Polytropic gas sphere
Lane–Emden equation
Truncated M-fractional derivative
White dwarfs
title Stellar structure via truncated M-fractional Lane–Emden solutions
title_full Stellar structure via truncated M-fractional Lane–Emden solutions
title_fullStr Stellar structure via truncated M-fractional Lane–Emden solutions
title_full_unstemmed Stellar structure via truncated M-fractional Lane–Emden solutions
title_short Stellar structure via truncated M-fractional Lane–Emden solutions
title_sort stellar structure via truncated m fractional lane emden solutions
topic Polytropic gas sphere
Lane–Emden equation
Truncated M-fractional derivative
White dwarfs
url https://doi.org/10.1038/s41598-025-96734-9
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