Analytical solution to the fractional polytropic gas spheres

  • Mohamed I. Nouh
  • Emad A-B. Abdel-Salam
Regular Article


The Lane-Emden equation can be used to model stellar interiors, star clusters and many configurations in astrophysics. Unfortunately, there is an exact solution only for the polytropic indices n = 0, 1 and 5. In the present paper, a series solution for the fractional Lane-Emden equation is presented. The solution is performed in the frame of modified Rienmann Liouville derivatives. The obtained results recover the well-known series solutions when \( \alpha =1\). The fractional model of n = 3 is calculated and the mass-radius relation, density ratio, pressure ratio and temperature ratio are investigated. The fractional star appears much different than the integer star, as it is denser, more stressed and hotter than the integer star.


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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Physics, College of ScienceNorthern Border UniversityArarSaudi Arabia
  2. 2.Department of AstronomyNational Research Institute of Astronomy and GeophysicsHelwan, CairoEgypt
  3. 3.Department of Mathematics, Faculty of ScienceAssiut UniversityEl-KharjaEgypt

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