Dynamical analysis of discrete time equations with a generalized order

Some natural phenomena that arise in nonlinear sciences can be sometimes discussed using discrete-time systems. In this work, we investigate the periodicity, boundedness, oscillation, stability, and some exact solutions of nonlinear difference equations with generalized order. Exact solutions are extracted using the traditional iteration and the modulus operator. The stability of the equilibrium points is examined using some well-known theorems. Some numerical examples are also introduced to confirm the validity of the theoretical work. We use MATLAB to implement the numerical part. The used technique can be easily utilized to deal with other rational recursive problems.