Dynamics and general form of the solutions of rational difference equations
Volume 34, Issue 4, pp 424--437
https://dx.doi.org/10.22436/jmcs.034.04.08
Publication Date: April 11, 2024
Submission Date: December 14, 2023
Revision Date: February 19, 2024
Accteptance Date: February 27, 2024
Authors
E. M. Elsayed
- Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.
- Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt.
F. A. Al-Rakhami
- Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.
- Department of Mathematics, Faculty of Science, Thamar University, Dhamar, Yemen.
N. M. Seyam
- Mathematics Sciences Department, College of Applied Science, Umm al-Qura University, Saudi Arabia.
Abstract
The main objective of this article is to find the general solution to some
special cases of the fractional recursive equation%
\[
\Psi_{n+1}=\frac{\alpha \Psi_{n-1}\Psi_{n-5}}{\Psi_{n-3}(\beta+\delta \Psi
_{n}\Psi_{n-1}\Psi_{n-4}\Psi_{n-5})},~ n=0,1,2,\ldots,
\]
where \(\alpha,\beta\) and \(\delta\) are arbitrary real numbers. Furthermore, the
solution's qualitative behavior is explored, such as local and global
stability. For some situations, we have discovered periodic solutions. We also
offered numerical examples to demonstrate our results.
Share and Cite
ISRP Style
E. M. Elsayed, F. A. Al-Rakhami, N. M. Seyam, Dynamics and general form of the solutions of rational difference equations, Journal of Mathematics and Computer Science, 34 (2024), no. 4, 424--437
AMA Style
Elsayed E. M., Al-Rakhami F. A., Seyam N. M., Dynamics and general form of the solutions of rational difference equations. J Math Comput SCI-JM. (2024); 34(4):424--437
Chicago/Turabian Style
Elsayed, E. M., Al-Rakhami, F. A., Seyam, N. M.. "Dynamics and general form of the solutions of rational difference equations." Journal of Mathematics and Computer Science, 34, no. 4 (2024): 424--437
Keywords
- Solutions expressions of difference equation
- local and global stability
- periodic solution
MSC
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