# Stability of a fractional difference equation of high order

Volume 12, Issue 2, pp 65--74
Publication Date: October 12, 2018 Submission Date: July 16, 2018 Revision Date: September 24, 2018 Accteptance Date: September 26, 2018
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### Authors

M. A. El-Moneam - Mathematics Department, Faculty of Science, Jazan University, Saudi Arabia. Tarek F. Ibrahim - Mathematics Department, College of Sciences and Arts for Girls in sarat Abida, King Khalid University, Saudi Arabia. - Mathematics Department, Faculty of Science, Mansoura University, Mansoura, Egypt. S. Elamody - Mathematics Department, Faculty of Science, Jazan University, Saudi Arabia.

### Abstract

In this paper we investigate the local stability, global stability, and boundedness of solutions of the recursive sequence% $x_{n+1}=x_{n-p}\ \left( \frac{2\ x_{n-q}\ +a\ x_{n-r}}{x_{n-q}\ +a\ x_{n-r}}% \right),$ where $x_{-q+k}\ \neq -a\ x_{-r+k}$ for $k=0,1,\dots,\min (q,r) , a\in \mathbb{R},\ p ,q, r \geq 0$ with the initial condition $x_{-p},x_{-p+1} ,\dots, x_{-q},$ $x_{-q+1} ,\dots, x_{-r},x_{-r+1} ,\dots, x_{-1}$ and $x_{0}\in (0,\infty )$. Some numerical examples will be given to illustrate our results.

### Share and Cite

##### ISRP Style

M. A. El-Moneam, Tarek F. Ibrahim, S. Elamody, Stability of a fractional difference equation of high order, Journal of Nonlinear Sciences and Applications, 12 (2019), no. 2, 65--74

##### AMA Style

El-Moneam M. A., Ibrahim Tarek F., Elamody S., Stability of a fractional difference equation of high order. J. Nonlinear Sci. Appl. (2019); 12(2):65--74

##### Chicago/Turabian Style

El-Moneam, M. A., Ibrahim, Tarek F., Elamody, S.. "Stability of a fractional difference equation of high order." Journal of Nonlinear Sciences and Applications, 12, no. 2 (2019): 65--74

### Keywords

• Difference equations
• prime period two solution
• boundedness character
• locally asymptotically stable
• global attractor
• global stability
• high orders

•  39A10
•  39A11
•  39A99
•  34C99

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