Conformable fractional isothermal gas spheres

Yousif, Eltayeb A.; Adam, A. M. A.; Hassaballa, Abaker A.; Nouh, M. I.

doi:10.1016/j.newast.2020.101511

Cited by 8 publications

(8 citation statements)

References 24 publications

(20 reference statements)

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“…Our calculations are done for 80 x  and the range of the fractional parameter 0.75 1   with step 0.1. For the integer case ( 1  = ), the comparison between the Emden function computed according to the series solution and the numerical one is in good agreement, Yousif et al (2021). Fractional models for the isothermal gas sphere could be computed using Equations ( 3) to ( 5) for the mass, radius, and density.…”

Section: Data Preparationmentioning

confidence: 63%

“…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.…”

Section: Introductionmentioning

confidence: 99%

“…where K is the pressure constant. By implementing the principles of the conformable derivatives Khalil et al (2014, Yousif et al (2021 derived the conformable second-order nonlinear differential equation that describes the isothermal gas sphere as…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Artificial Neural Network Modeling of the Conformable Fractional Isothermal Gas Spheres

Azzam

Abdel-Salam

Nouh

2021

RMxAA

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The isothermal gas sphere is a particular type of Lane-Emden equation and is used widely to model many problems in astrophysics, like the formation of stars, star clusters and galaxies. In this paper, we present a computational scheme to simulate the conformable fractional isothermal gas sphere using an artificial neural network (ANN) technique, and we compare the obtained results with the analytical solution deduced using the Taylor series. We performed our calculations, trained the ANN, and tested it using a wide range of the fractional parameter. Besides the Emden functions, we calculated the mass-radius relations and the density profiles of the fractional isothermal gas spheres. The results obtained show that the ANN could perfectly simulate the conformable fractional isothermal gas spheres.

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Section: Data Preparationmentioning

confidence: 63%

Section: Introductionmentioning

confidence: 99%

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Artificial Neural Network Modeling of the Conformable Fractional Isothermal Gas Spheres

Azzam

Abdel-Salam

Nouh

2021

RMxAA

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“…The prospect of using such local fractional derivatives as Conformable Fractional Derivatives (CFD) in cosmology and astrophysics is confirmed by work [101], where the fractional equation of an isothermal gas sphere is written and solved. to conformable fractional isothermal gas spheres In this study, the fractional form of isothermal Lane-Emden for the CFD isothermal gas sphere is considered using the power series method and obtain a recurrence relation for the power series coefficient.…”

Section: Some Recent Studies Of Facmentioning

confidence: 99%

Fractional-order derivatives in cosmological models of accelerated expansion

Shchigolev

2021

Preprint

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In this brief review, we present the results of the fractional differential approach in cosmology in the context of the exact models of cosmological accelerated expansion obtained by several authors to date. Most of these studies are devoted to the problem of introducing fractional derivatives or fractional integrals into the classical General Relativity (GR). There are several observational and theoretical motivations to investigate the modified or alternative theories of GR. Among other things, we cover General Relativity modified by a phenomenological approach dealing with fractional calculus. At the same time, a sufficiently large number of exact solutions of the cosmological equations modified by this approach were obtained. Some of these models may be especially relevant in the light of solving the problem of late accelerated expansion of the universe. These studies are largely motivated by rapid progress in the field of observational cosmology that now allows, for the first time, precision tests of fundamental physics on the scale of the observable Universe. The purpose of this review is to provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a self-contained, comprehensive and up-to-date introduction to the subject as a whole.

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“…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].…”

Section: Introductionmentioning

confidence: 99%