A novel fractal-fractional analysis of the stellar helium burning network using extended operational matrix method. (17th February 2023)

• Record Type: Journal Article
• Authors: Shloof, A M; Senu, N; Ahmadian, A; Nouh, M I; Salahshour, S
• Is Part Of: Physica scripta. Volume 98:Number 3(2023)
• Publication Date: 2023-02-17
• Subjects: fractal-fractional derivatives -- systems of fractal-fractional order differential equations -- stellar helium burning network -- operational matrix; Physics -- Periodicals; 530.05
• DOI: 10.1088/1402-4896/acba5d
• Languages: English
• ISSNs: 0031-8949

Abstract

Abstract: The second stage, in which the star uses nuclear fuel in its interior, represents the helium burning phase. At that stage, three elements are synthesised: carbon, oxygen, and neon. This paper aims 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. The product abundances of the four elements (helium, carbon, oxygen and neon) were obtained in a form of divergent series. These 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 fractal-fractional parameters' influence 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.