DYNAMICAL BEHAVIOR AND SOLUTION OF NONLINEAR DIFFERENCE EQUATION VIA FIBONACCI SEQUENCE

E. M. Elsayed; Faris Alzahrani; Ibrahim Abbas; N. H. Alotaibi

doi:10.11948/20190143

2020 Volume 10 Issue 1

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E. M. Elsayed, Faris Alzahrani, Ibrahim Abbas, N. H. Alotaibi. DYNAMICAL BEHAVIOR AND SOLUTION OF NONLINEAR DIFFERENCE EQUATION VIA FIBONACCI SEQUENCE[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 282-296. doi: 10.11948/20190143

Citation:

E. M. Elsayed, Faris Alzahrani, Ibrahim Abbas, N. H. Alotaibi. DYNAMICAL BEHAVIOR AND SOLUTION OF NONLINEAR DIFFERENCE EQUATION VIA FIBONACCI SEQUENCE[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 282-296. doi: 10.11948/20190143

DYNAMICAL BEHAVIOR AND SOLUTION OF NONLINEAR DIFFERENCE EQUATION VIA FIBONACCI SEQUENCE

1.
King Abdulaziz University, Faculty of Science, Mathematics Department, P. O. Box 80203, Jeddah 21589, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Mansoura University

Author Bio: Email address: faris.kau@hotmail.com(F. Alzahrani); Email address: ibrabbas7@gmail.com(I. Abbas); Email address: n.h.ob@hotmail.com(N. H. Alotaibi)
Corresponding author: Email address: emmelsayed@yahoo.com(E. M. Elsayed)
Fund Project: This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia under grant no

Abstract

Abstract

In this paper, we study the behavior of the difference equation $x_{n+1}=ax_{n}+\dfrac{bx_{n}x_{n-1}}{cx_{n-1}+dx_{n-2}},~n=0,1,\ldots,$ where the initial conditions $x_{-2},\ x_{-1},\ x_{0}$ are arbitrary positive real numbers and $a,b,c,d$ are positive constants. Also, we give the solution of some special cases of this equation.
- Stability /
- boundedness /
- solution of difference equations
MSC: 39A10

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References

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