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Stellar structure via truncated M-fractional Lane-Emden solutions.

Mohamed I Nouh1, Emad A-B Abdel-Salam2, Abaker A Hassaballa3,4

  • 1Astronomy Department, National Research Institute of Astronomy and Geophysics, Helwan, Cairo, 11421, Egypt.

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|April 11, 2025
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Summary

This study introduces a fractional generalization of the Lane-Emden equation using truncated M-fractional derivatives. Fractional models reveal that stellar radius and mass decrease with fractional parameters, impacting stellar structure insights.

Keywords:
Lane–Emden equationPolytropic gas sphereTruncated M-fractional derivativeWhite dwarfs

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Area of Science:

  • Astrophysics and Computational Physics
  • Stellar Structure and Evolution
  • Fractional Calculus Applications

Background:

  • The Lane-Emden equation models self-gravitating, spherically symmetric polytropic stars in hydrostatic equilibrium.
  • It is fundamental in astrophysics for understanding normal stars, white dwarfs, and celestial systems.
  • Conventional models lack the framework to incorporate complex fractional behaviors in stellar physics.

Purpose of the Study:

  • To introduce a novel fractional generalization of the Lane-Emden equation using truncated M-fractional derivatives (TMD).
  • To explore the impact of fractional calculus on the structural properties of polytropic gas spheres.
  • To develop new polytropic stellar models beyond the classical Lane-Emden framework.

Main Methods:

  • Formulation of the truncated M-fractional Lane-Emden equation (TMD-LEE).
  • Application of the accelerated power series approach to solve the TMD-LEE.
  • Generation of fractional polytropic models across various polytropic indices.

Main Results:

  • Solutions to the TMD-LEE were obtained, creating fractional polytropic models.
  • The initial zero of the fractional Lane-Emden function increases as fractional parameters decrease.
  • Stellar radius and mass in these fractional models decrease with decreasing fractional parameters.

Conclusions:

  • Fractional factors significantly influence the structural scaling of stars, offering new insights into stellar physics.
  • The developed fractional polytropic models expand classical polytrope theory.
  • These models have potential applications in understanding complex astrophysical phenomena within fractional calculus frameworks.