Analytical solution to the fractional polytropic gas spheres

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 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 1   . 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.

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.…”

Conformable fractional polytropic gas spheres

“…with Equations ( 21) to ( 22). First, we compare the present solution with the solution presented by Nouh and Abdel-Salam (2018), where they have simulated the fractional polytropic gas sphere via accelerated series expansion; the results indicated that the fractional polytropic sphere is smaller than the integer one. We updated our code to the conformable formulations, so the modified code contains the two series expansions.…”

Global Mittag—Leffler Synchronization for Neural Networks Modeled by Impulsive Caputo Fractional Differential Equations with Distributed Delays

“…Over the last few decades, fractional differential equations have gained considerable importance and attention due to their applications in science and engineering, i.e., in control, in stellar interiors, star clusters [1], in electrochemistry, in viscoelasticity [2] and in optics [3]. For example, the control of mechanical systems is currently one of the most active fields of research and the use of fractional order calculus increases the flexibility of controlling any system from a point to a space.…”

“…The idea of this approach is based on the dependence of the Caputo fractional derivative on the initial time point of the interval of differential equation, i.e., the lower limit of the Caputo fractional derivative is changing at each moment of impulse of the differential equation. Sometimes, Equation (1) in this case is written by…”