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arXiv · 1604.03142

Analytical Solution to the Fractional Polytropic Gas Spheres

Mohamed I. Nouh·Emad A-B. Abdel-Salam
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Abstract

Lane-Emden equation could be used to model stellar interiors, star clusters and many configurations in astrophysics. Unfortunately, there is an exact solution only for the polytropic index and . 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 . Fractional model of n=3 has been calculated and mass-radius relation, density ratio, pressure ratio and temperature ratio have been investigated. We found that the fractional star has a smaller volume and mass than that of the integer star.

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Mohamed I. Nouh, Emad A-B. Abdel-Salam. 2016-04-11. Analytical Solution to the Fractional Polytropic Gas Spheres. https://doi.org/10.1140/epjp/i2018-11980-5

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