Geodesic
Stability of a fractional difference equation of high order
El-Moneam, M. A. 1 ; Ibrahim, Tarek F. 2 ; Elamody, S. 1
1 Mathematics Department, Faculty of Science, Jazan University, Saudi Arabia
2 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
Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 2, p. 65-74.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.012.02.01
Classification : 39A10, 39A11, 39A99, 34C99
Keywords: Difference equations, prime period two solution, boundedness character, locally asymptotically stable, global attractor, global stability, high orders

El-Moneam, M. A.  1 ; Ibrahim, Tarek F.  2 ; Elamody, S.  1

1 Mathematics Department, Faculty of Science, Jazan University, Saudi Arabia
2 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 
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     title = {Stability of a fractional difference equation of high order},
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El-Moneam, M. A. ; Ibrahim, Tarek F. ; Elamody, S. . Stability of a fractional difference equation of high order. Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 2, p. 65-74. doi : 10.22436/jnsa.012.02.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.02.01/

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