# Expressions and dynamical behavior of solutions of a class of rational difference equations of fifteenth-order

Volume 25, Issue 1, pp 10--22
Publication Date: May 04, 2021 Submission Date: January 28, 2021 Revision Date: February 24, 2021 Accteptance Date: March 18, 2021
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### Authors

A. M. Ahmed - Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka, Jouf, Saudi Arabia. - Department of Mathematics, Faculty of Science, Al Azhar University, Nasr City 11884, Cairo, Egypt. Samir Al Mohammady - Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka, Jouf, Saudi Arabia. - Department of Mathematics, Faculty of Science, Helwan University, Helwan 11795, Egypt. Lama Sh. Aljoufi - Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka, Jouf, Saudi Arabia.

### Abstract

The main goal of this paper, is to obtain the forms of the solutions of the following nonlinear fifteenth-order difference equations $x_{n+1}=\frac{x_{n-14}}{\pm 1\pm x_{n-2}x_{n-5}x_{n-8}x_{n-11}x_{n-14}},\ \ \ \ n=0,1,2,\ldots,$ where the initial conditions $x_{-14},x_{-13},\ldots,x_{0}$ are arbitrary real numbers. Moreover, we investigate stability, boundedness, oscillation and the periodic character of these solutions. Finally, we confirm the results with some numerical examples and graphs by using Matlab program.

### Share and Cite

##### ISRP Style

A. M. Ahmed, Samir Al Mohammady, Lama Sh. Aljoufi, Expressions and dynamical behavior of solutions of a class of rational difference equations of fifteenth-order, Journal of Mathematics and Computer Science, 25 (2022), no. 1, 10--22

##### AMA Style

Ahmed A. M., Mohammady Samir Al, Aljoufi Lama Sh., Expressions and dynamical behavior of solutions of a class of rational difference equations of fifteenth-order. J Math Comput SCI-JM. (2022); 25(1):10--22

##### Chicago/Turabian Style

Ahmed, A. M., Mohammady, Samir Al, Aljoufi, Lama Sh.. "Expressions and dynamical behavior of solutions of a class of rational difference equations of fifteenth-order." Journal of Mathematics and Computer Science, 25, no. 1 (2022): 10--22

### Keywords

• Recursive sequence
• oscillation
• semicycles
• stability
• periodicity
• solutions of difference equations

•  39A10
•  39A22
•  39A23

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