Conformable fractional polytropic gas spheres

Abstract

Lane -Emden differential equation of the polytropic gas sphere could be used to construct simple models of stellar structures, star clusters and many configurations in astrophysics.This differential equation suffers from the singularity at the center and has an exact solution only for the polytropic index n=0, 1 and 5 . In the present paper, we present an analytical solution to the fractional polytropic gas sphere via accelerated series expansion. The solution is performed in the frame of conformable fractional derivatives. The calculated models recover the well-known series of solutions when 1   . Physical parameters such as mass-radius relation, density ratio, pressure ratio and temperature ratio for different fractional models have been calculated and investigated.We found that the present models of the conformable fractional stars have smaller volume and mass than that of both the integer star and fractional models performed in the frame of modified Rienmann Liouville derivatives.

Modeling fractional polytropic gas spheres using artificial neural network

“…The Newtonian stellar polytrope's fractional version was investigated by [12] for the fractional white dwarf model, [13] for the incompressible gas sphere, [14] for the fractional isothermal gas sphere. Nouh and Abdel-Salam [15] and [16] constructed fractional polytropic stellar models for white dwarfs with n=1.5 and solar type stars n=3. For n =3, [15][16] showed that solar-like stars could be modeled by dividing the interior into two layers with different fractional parameters.…”

“…Nouh and Abdel-Salam [15] and [16] constructed fractional polytropic stellar models for white dwarfs with n=1.5 and solar type stars n=3. For n =3, [15][16] showed that solar-like stars could be modeled by dividing the interior into two layers with different fractional parameters.…”

Artificial Neural Network Modeling of the Conformable Fractional Isothermal Gas Spheres

“…Many methods were proposed to solve these equations. The fractional polytropic models were investigated by El-Nabulsi (2011) for white dwarf stars, Bayin and Krisch (2015) for the incompressible gas sphere, Abdel-Salam and Nouh (2016) and Yousif et al (2021) for the isothermal gas sphere. Ana-lytical solutions to the fractional Lane-Emden equations using series expansion and Adomian decomposition methods were introduced by Nouh and Abdel-Salam (2018a), Abdel-Salam and Nouh (2020), Nouh andAbdel-Salam (2018b), and.…”

New Families of Solutions for the Space-Time Fractional Burgers’ Equation

“…In the last few years, there are considerable and numerous models in the literature are formulated in terms of conformable fractional derivatives [11][12][13][14][15].…”