MMN-3385

On the solutions of a system of (2p+1) difference equations of higher order

• A. Khelifa, University of Mohamed Seddik Ben Yahia, LMAM Laboratory and Department of Mathematics, Jijel, Algeria, amkhelifa@yahoo.com
• Y. Halim, Abdelhafid Boussouf University of Mila, Department of Mathematics and Computer Science, and LMAM Laboratory, University of Mohamed Seddik Ben Yahia, Jijel, Algeria, halyacine@yahoo.fr
• M. Berkal, University of Alicante, Department of Applied Mathematics, Alicante, Spain, mb299@gcluad.ua.es

Abstract

In this paper we represents the well-defined solutions of the system of the higher-order rational difference equations \begin{equation*} x^{(j)}_{n+1}=\dfrac{1+2x^{(j+1)mod(2p+1)}_{n-k}}{3+x^{(j+1)mod(2p+1)}_{n-k}},\quad n, k, p \in \mathbb{N}_{0} \end{equation*} in terms of Fibonacci and Lucase sequences, where the initial values $x^{(j)}_{-k}, x^{(j)}_{-k+1}$,\\$\ldots, x^{(-1)}_0$ and $x^{(i)}_0$, $j=1,2,\ldots,2p+1$, do not equal -3. Some theoretical explanations related to the representation for the general solution are also given.

Vol. 22 (2021), No. 1, pp. 331-350
DOI: 10.18514/MMN.2021.3385