Approximate solution for system of fractional non-linear dynamical marriage model using Bernstein polynomials

Volume 10, Issue 3, pp 865--873 http://dx.doi.org/10.22436/jnsa.010.03.02

Publication Date: March 20, 2017 Submission Date: October 14, 2015

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Authors

Mohamed M. Khader - Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh: 11566, Saudi Arabia. - Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt. Rubayyi T. Alqahtani - Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh: 11566, Saudi Arabia.

Abstract

This paper is devoted to present the approximate solutions with helping of an efficient numerical method for the nonlinear coupled system of dynamical marriage model in the fractional of Riemann-Liouville sense (FDMM). The proposed system describes the dynamics of love affair between a couple. The proposed method is dependent on the use of useful properties of the operational matrices of Bernstein polynomials. The operational matrices for the fractional integration in the Riemann-Liouville sense and the product are used to reduce FDMM to the solution of non-linear system of algebraic equations using Newton iteration method. Numerical simulation is given to show the validity and the accuracy of the proposed algorithm. We introduce a comparison with the obtained solution using Runge-Kutta method.

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Keywords

• Fractional dynamical model of marriage
• Riemann-Liouville fractional derivatives
• operational matrix
• Bernstein polynomials.

MSC

•  41A04
•  65N20

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