Qualitative analysis for two fractional difference equations

Abstract

Some difference equations are generally studied by investigating their long behaviours rather than their exact solutions. The proposed equations cannot be solved analytically. Hence, this article discusses the main qualitative behaviours of two rational difference equations. Some appropriate hypotheses are examined and given to show the local and global attractivity. Special cases from the considered equations are solved analytically. The periodicity is also proved in this work. We also illustrate the achieved results in some 2D figures.

Periodic solutions and stability of eighth order rational difference equations

“…In [5], the authors discussed the stability, periodicity and some solutions of the difference equation…”

Qualitative Behavior of Solutions of Tenth-Order Recursive Sequence Equation

“…Al-Matrafi and Al-Zubaidi [4] achieved global and local stability and forms of positive periodic solutions for two types of recursive equations:…”

Dynamical Behavior and Solutions of Nonlinear Difference Equations of Twentieth Order Lama Sh. Aljoufi and M. B. Almatrafi

“…Finally, Kara and Yazlik [8] solved a (k + l)-order difference equation and presented the asymptotic approach of the obtained solutions of the equation when k = 3, and l = k. More results about such equations can be simply obtained in refs. [9][10][11][12][13][14][15][16][17][18][19][20][21]. The essential purpose of this article is to discuss and present some qualitative behaviors such as the equilibrium points, local and global approaches, boundedness, and the analytic solutions of the nonlinear difference equations…”