Approximate solution for system of fractional non-linear dynamical marriage model using Bernstein polynomials
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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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ISRP Style
Mohamed M. Khader, Rubayyi T. Alqahtani, Approximate solution for system of fractional non-linear dynamical marriage model using Bernstein polynomials, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 3, 865--873
AMA Style
Khader Mohamed M., Alqahtani Rubayyi T., Approximate solution for system of fractional non-linear dynamical marriage model using Bernstein polynomials. J. Nonlinear Sci. Appl. (2017); 10(3):865--873
Chicago/Turabian Style
Khader, Mohamed M., Alqahtani, Rubayyi T.. "Approximate solution for system of fractional non-linear dynamical marriage model using Bernstein polynomials." Journal of Nonlinear Sciences and Applications, 10, no. 3 (2017): 865--873
Keywords
- Fractional dynamical model of marriage
- Riemann-Liouville fractional derivatives
- operational matrix
- Bernstein polynomials.
MSC
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