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Analytical solution to the fractional polytropic gas spheres

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Abstract.

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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Authors and Affiliations

  1. Department of Physics, College of Science, Northern Border University, Arar, Saudi Arabia

    Mohamed I. Nouh

  2. Department of Astronomy, National Research Institute of Astronomy and Geophysics, 17211, Helwan, Cairo, Egypt

    Mohamed I. Nouh

  3. Department of Mathematics, Faculty of Science, Assiut University, New Valley Branch, 72511, El-Kharja, Egypt

    Emad A-B. Abdel-Salam

Authors
  1. Mohamed I. Nouh
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  2. Emad A-B. Abdel-Salam
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Correspondence to Mohamed I. Nouh.

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Nouh, M.I., Abdel-Salam, E.AB. Analytical solution to the fractional polytropic gas spheres. Eur. Phys. J. Plus 133, 149 (2018). https://doi.org/10.1140/epjp/i2018-11980-5

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  • DOI: https://doi.org/10.1140/epjp/i2018-11980-5

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