Approximate solution for system of fractional nonlinear dynamical marriage model using Bernstein polynomials
Authors
Mohamed M. Khader
 Department of Mathematics and Statistics, College of Science, AlImam 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, AlImam 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 RiemannLiouville 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 RiemannLiouville
sense and the product are used to reduce FDMM to the solution of nonlinear 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 RungeKutta method.
Keywords
 Fractional dynamical model of marriage
 RiemannLiouville fractional derivatives
 operational matrix
 Bernstein polynomials.
MSC
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