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

Abstract

In this paper we represent the well-defined solutions of the system of the higher-order rational difference equationsin terms of Fibonacci and Lucas sequences, where the initial valuesdo not equal -3. Some theoretical explanations related to the representation for the general solution are also given.

Global Behavior of Solutions to a Higher-Dimensional System of Difference Equations with Lucas Numbers Coefficients

“…Recently, there has been a growing interest in the study of finding closed-form solutions of difference equations and systems of difference equations. Some of the forms of solutions of these equations are representable via wellknown integer sequences such as Fibonacci numbers (see, for example [26,32]), Horadam numbers (see, for example, [30,31]), Lucas numbers (see, for example [25,27,33]), Pell numbers and Padovan numbers (see, for example [34][35][36]), But in this paper, we present the solution in the form of Lucas sequences.…”

Solvability of a Second-Order Rational System of Difference Equations

“…Recently, there has been a growing interest in the study of finding closed-form solutions of difference equations and systems of difference equations. Some of the forms of solutions of these equations are representable via well-known integer sequences such as Fibonacci numbers [1,2], Horadam numbers [3], Lucas numbers [4,5], and Padovan numbers [6]. For more on Fibonacci and Lucas numbers, one can see [7,8], for more on difference equations and systems of difference equations solvable in closed form, one can see [9]- [24].…”