Conformable Fractional Models of the Stellar Helium Burning via Artificial Neural Networks

Abdel-Salam, Emad A.-B.; Nouh, M. I.; Azzam, Yosry A.; Jazmati, M. S.

doi:10.1155/2021/6662217

Cited by 4 publications

(3 citation statements)

References 31 publications

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“…In a series of LorenzoHartley function, Chaurasia and Pandey [17] solved the fractional kinetic equations. The fractional kinetic equations were solved via artificial neural networks (ANNs) by Abdel-Salam et al [18].…”

Section: Introductionmentioning

confidence: 99%

A novel fractal-fractional analysis of the stellar helium burning network using extended operational matrix method

Shloof¹,

Senu²,

Ahmadian³

et al. 2023

Phys. Scr.

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The second stage, in which the star uses the nuclear fuel in its interior, represents the helium burning phase. At that stage, three elements are synthesised, which are carbon, oxygen and neon. The purpose of this paper is to establish a numerical solution for the helium burning system (HBN) fractal fractional diﬀerential equations (FFDEs). The extended operative matrix method (OM) is employed in the solution of a system of diﬀerential equations. and the product abundances, namely helium, carbon, oxygen and neon. The product abundances of the four elements were obtained in a form of divergent series. This divergent series are then accelerated using Euler-Abell transformation (EUAT) and Pade approximation (EUAT-PA) to obtain more reliable results. Nine fractal-fractional (FF) gas models are calculated and the inﬂuence of fractal-fractional parameters on product abundances is discussed. The ﬁndings show that modeling nuclear burning networks with the OM fractal-fractional derivative produces excellent results, establishing it as an accurate, resilient, and trustworthy approach, and the fractional HB models can have a considerable impact on stellar model calculations.

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Section: Introductionmentioning

confidence: 99%

A novel fractal-fractional analysis of the stellar helium burning network using extended operational matrix method

Shloof¹,

Senu²,

Ahmadian³

et al. 2023

Phys. Scr.

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“…There are a large number of published studies describing various methods and computational algorithms that introduce analytical/numerical solutions to the LE equation as Runge-Kutta type methods [6], Homotopy perturbation methods [7] and [8]; Adomian decomposition methods [9] and [10]; accelerated series expansion [11]; the MC integration [5]; genetic algorithm [12]; artificial neural networks [13][14][15] and spectral collocation approach [16,17].…”

Section: Introductionmentioning

confidence: 99%

A novel numerical solution to lane-emden type equations using monte carlo technique

El-Essawy,

Nouh,

Soliman

et al. 2023

Phys. Scr.

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Monte Carlo (MC) methods are increasingly recognized as severe in many computational scientific fields and have diverse applications in many branches of science. This paper systematically provides two computational algorithms based on MC methods to solve different forms of Lane-Emden (LE) type equations. The proposed algorithms introduce solutions to 11 LE equations under various complex conditions. The performance and comparative study of numerical solutions based on the MC algorithms were computationally analyzed using other numerical/analytical methods available in the literature. We find that the MC solutions agree with the exact or Runge–Kutta solutions and different numerical methods applied to solve these equations.

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“…Azzam et al (2021) used an artificial neural network (ANN) approach and simulate the conformable fractional isothermal gas spheres and compared them with the results of the analytical solution deduced using the Taylor series. Abdel-Salam et al (2021) presented the neural network (NN) mathematical model and developed a neural network approach for simulating the helium burning network using a feed-forward mechanism.…”

Section: Introductionmentioning

confidence: 99%

Ann and Analytical Solutions to Relativistic Isothermal Gas Spheres

Nouh

Azzam

Abdel-Salam

et al. 2022

RMxAA

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Relativistic isothermal gas spheres are a powerful tool to model many astronomical objects, like compact stars and clusters of galaxies. In the present paper, we introduce an artificial neural network (ANN) algorithm and Taylor series to model the relativistic gas spheres using Tolman-Oppenheimer-Volkoff differential equations (TOV). Comparing the analytical solutions with the numerical ones revealed good agreement with maximum relative errors of 10−3. The ANN algorithm implements a three-layer feed-forward neural network built using a back-propagation learning technique that is based on the gradient descent rule. We analyzed the massradius relations and the density profiles of the relativistic isothermal gas spheres against different relativistic parameters and compared the ANN solutions with the analytical ones. The comparison between the two solutions reflects the efficiency of using the ANN to solve TOV equations.

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Conformable Fractional Models of the Stellar Helium Burning via Artificial Neural Networks

Cited by 4 publications

References 31 publications

A novel fractal-fractional analysis of the stellar helium burning network using extended operational matrix method

A novel fractal-fractional analysis of the stellar helium burning network using extended operational matrix method

A novel numerical solution to lane-emden type equations using monte carlo technique

Ann and Analytical Solutions to Relativistic Isothermal Gas Spheres

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