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In this paper, we study the equilibrium points, local asymptotic stability of equilibrium points, global behavior of equilibrium points, boundedness and periodicity of the rational recursive sequence w n + 1 = w n − p α + β w n / γ w n + δ w n − r , where γ w n ≠ − δ w n − r for r ∈ 0 , ∞ , α , β , γ , δ ∈ 0 , ∞ , and r > p ≥ 0. With initial values w − p , w − p + 1 , ... , w − r , w − r + 1 , ... , w − 1 , and w 0 are positive real numbers. Some numerical examples are given to verify our theoretical results. [ABSTRACT FROM AUTHOR]

In this study, we construct a convergent algorithm for generating an approximate analytic solution for the fractional HIV infection of CD 4 + T cells with Atangana–Baleanu fractional derivatives in the Caputo sense. We compute the solution by utilizing the fractional homotopy analysis transform method (FHATM) and achieved a convergence region of the solution by employing an auxiliary parameter. Moreover, we apply a numerical scheme proposed by Toufik and Atangana for solving this kind of problem and compared with our results. A good agreement between the new algorithm and the numerical scheme is remarkable. The solution via the present algorithm can be obtained without any linearization or discretization which makes it reliable and easy to apply. [ABSTRACT FROM AUTHOR]

In this paper, we study the global dynamics of three higher-order exponential systems of rational difference equations. This suggested work considerably extends and improves some existing results in the literature. [ABSTRACT FROM AUTHOR]

The structure of the solutions for the system nonlinear difference equations xn+1=ynyn-2/(xn-1+yn-2), yn+1=xnxn-2/(±yn-1±xn-2), n=0,1,…, is clarified in which the initial conditions x-2, x-1, x0, y-2, y-1, y0 are considered as arbitrary positive real numbers. To exemplify the theoretical discussion, some numerical examples are presented. [ABSTRACT FROM AUTHOR]

By employing a generalized Riccati technique and an integral averaging technique, some new oscillation criteria are established for the second order nonlinear forced differential equation with damping. These results extend, improve, and unify some known oscillation criteria in the existing literature. [ABSTRACT FROM AUTHOR]

Some new oscillation criteria are given for second-order nonlinear differential equations with variable coefficients. Our results generalize and extend some of the well-known results in the literatures. Some examples are considered to illustrate the main results. [ABSTRACT FROM AUTHOR]