Closed-Form Solution of a Rational Difference Equation

In this paper, we study the solution of the difference equation Ω m + 1 = Ω m − 7 q + 6 / 1 + ∏ t = 0 5 Ω m − q + 1 t − q , where the initials are positive real numbers.

Dynamics and Solutions’ Expressions of a Higher-Order Nonlinear Fractional Recursive Sequence

The principle purpose of this article is to examine some stability properties for the fixed point of the below rational difference equation U n + 1 = ξ U n − 8 + ε U n − 8 2 / μ U n − 8 + κ U n − 17 where ξ , ε , μ , and κ are arbitrary real numbers. Moreover, solutions for some special cases of the proposed difference equation are introduced.

On the Solutions of Three-Dimensional Rational Difference Equation Systems

In this paper, we are interested in a technique for solving some nonlinear rational systems of difference equations of third order, in three-dimensional case as a special case of the following system: x n + 1 = y n z n − 1 / y n ± x n − 2 , y n + 1 = z n x n − 1 / z n ± y n − 2 , and z n + 1 = x n y n − 1 / x n ± z n − 2 with initial conditions x − 2 , x − 1 , x 0 , y − 2 , y − 1 , y 0 , z − 2 , z − 1 , and z 0 are nonzero real numbers. Moreover, we study some behavior of the systems such as the boundedness of solutions for such systems. Finally, we present some numerical examples by giving some numerical values for the initial values of each case. Some figures have been given to explain the behavior of the obtained solutions in the case of numerical examples by using the mathematical program MATLAB to confirm the obtained results.