Approximate Solution to the Fractional Second-Type Lane-Emden Equation

Abstract

Abstract.The spherical isothermal Lane-Emden equation is a second order non-linear differential equation

Computational method for a fractional model of the helium burning network

“…Nowadays, generalizations of some of the basic differential equations in physics led to new and more deep insight to the macroscopic phenomena in a wide range of areas like anomalous diffusion, signal processing and quantum mechanics (Podlubny 1999;Sokolov et al 2002;Kilbas et al 2006;Laskin 2000). In astrophysics, El-Nabulsi (2011) considered a fractional equation of state for white dwarf stars; Bayian and Krisch (2015) have investigated the fractional versions of the stellar structure equations for non-radiating spherical objects, Abdel-Salam and Nouh (2016) and Nouh and Abdel-Salam (2017) introduced a series solution to the fractional isothermal and polytropic gas spheres and obtained a solution converges to the surface of the sphere with a few series terms when compared with the solution of the integer one.…”

Conformable fractional isothermal gas spheres

“…The results for the radii, masses, and central density of the conformable models are listed in Table 2. We observed that the conformable fractional models have less volume and less mass than both the integer models and the fractional models computed based on the scheme presented by Abdel-Salam and Nouh (2016). The dramatic change in both the mass and radius of the models indicate the huge compression of the material inside the star.…”

“…The fractional Emden functions ( R u ) computed by Abdel-Salam and Nouh (2016) are plotted (dashed lines) along with the conformable one ( . This may come from the difference in the nature between the conformable and the mRFD.…”

“…The fractional Lane-Emden equations have been analysed by El-Nabulsi (2011) for the white dwarf stars, Bayian and Krisch (2015) for the incompressible gas sphere, Abdel-Salam and Nouh (2016) for the fractional isothermal gas sphere and Nouh and Abdel-Salam (2018) for the polytropic gas sphere, Abdel-Salam and for the conformable polytropic gas spheres.…”

“…The fractional isothermal gas sphere has been analyzed by Mizra (2009) who solved the fractional isothermal gas spheres starting by two terms series expansion and iterates till obtaining reasonable values for the Emden function near the center of the sphere. By implementing Riemann-Liouville concept of the fractional derivatives, the fractional version of the equation is studied by Abdel-Salam and Nouh (2016). developed a conformable Adomian decomposition method to obtain a divergent series solution for the isothermal gas spheres.…”