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THE REPRODUCING KERNEL ALGORITHM FOR NUMERICAL SOLUTION OF VAN DER POL DAMPING MODEL IN VIEW OF THE ATANGANA–BALEANU FRACTIONAL APPROACH

SHAHER MOMANI

Department of Mathematics and Sciences, College of Humanities and Sciences, Ajman University, Ajman, UAE

Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan

E-mail Address: s.momani@ajman.ac.ae

E-mail Address: s.momani@ju.edu.jo

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BANAN MAAYAH

Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan

E-mail Address: b.maayah@ju.edu.jo

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, and

OMAR ABU ARQUB

Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan

E-mail Address: o.abuarqub@bau.edu.jo

Corresponding author.

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https://doi.org/10.1142/S0218348X20400101Cited by:98 (Source: Crossref)

This article is part of the issue:

Special Issue on Fractal and Fractional with Applications to Nature
Guest Editors: Abdon Atangana, Emile Franc Goufo Ndongmo, José Francisco Gómez Aguilar, Muhammad Altaf Khan and Ilknur Koca

Abstract

The aim of this paper is to propose the Atangana–Baleanu fractional methodology for fathoming the Van der Pol damping model by using the reproducing kernel algorithm. To this end, we discuss the mathematical structure of this new approach and some other numerical properties of solutions. Furthermore, all needed requirements for characterizing solutions by applying the reproducing kernel algorithm are debated. In this orientation, modern trend and new computational algorithm in terms of analytic and approximate Atangana–Baleanu fractional solutions are proposed. Finally, numerical simulations in fractional emotion is constructed one next to the other with tabulated data and graphical portrayals.

Keywords:

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Vol. 28, No. 08

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History

Received 7 January 2020

Accepted 3 March 2020

Published: September 1, 2020

Information

This is an Open Access article in the “Special Issue on Fractal and Fractional with Applications to Nature” published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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THE REPRODUCING KERNEL ALGORITHM FOR NUMERICAL SOLUTION OF VAN DER POL DAMPING MODEL IN VIEW OF THE ATANGANA–BALEANU FRACTIONAL APPROACH

Abstract

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