A Numerical Algorithm for the Solutions of ABC Singular Lane–Emden Type Models Arising in Astrophysics Using Reproducing Kernel Discretization Method

Omar Abu Arqub, Mohamed S. Osman, Abdel-Haleem Abdel-Aty, Abdel-Baset A. Mohamed and Shaher Momani
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Omar Abu Arqub: Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan
Mohamed S. Osman: Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
Abdel-Haleem Abdel-Aty: Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia
Abdel-Baset A. Mohamed: Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam bin Abdulaziz University, Al-Aflaj 11942, Saudi Arabia
Shaher Momani: Department of Mathematics and Sciences, College of Humanities and Sciences, Ajman University, Ajman, UAE

Mathematics, 2020, vol. 8, issue 6, 1-15

Abstract: This paper deals with the numerical solutions and convergence analysis for general singular Lane–Emden type models of fractional order, with appropriate constraint initial conditions. A modified reproducing kernel discretization technique is used for dealing with the fractional Atangana–Baleanu–Caputo operator. In this tendency, novel operational algorithms are built and discussed for covering such singular models in spite of the operator optimality used. Several numerical applications using the well-known fractional Lane–Emden type models are examined, to expound the feasibility and suitability of the approach. From a numerical viewpoint, the obtained results indicate that the method is intelligent and has several features stability for dealing with many fractional models emerging in physics and mathematics, using the new presented derivative.

Keywords: Atangana–Baleanu–Caputo fractional derivative; fractional Lane–Emden type models; reproducing kernel discretization method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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