Browsing by Subject "boundedness"

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Access status: Open Access ,
On the asymptotic behavior of nonoscillatory solutions of certain fractional differential equations with positive and negative terms
(Wydawnictwa AGH, 2020) Graef, John R.; Grace, Said R.; Tunç, Ercan
This paper is concerned with the asymptotic behavior of the nonoscillatory solutions of the forced fractional differential equation with positive and negative terms of the form $^{C}D_{c}^{\alpha}y(t)+f(t,x(t))=e(t)+k(t)x^{\eta}(t)+h(t,x(t)),$ where $t\geq c \geq 1$, $\alpha \in (0,1)$, $\eta \geq 1$ is the ratio of positive odd integers, and $^{C}D_{c}^{\alpha}y$ denotes the Caputo fractional derivative of $y$ of order $\alpha$. The cases $y(t)=(a(t)(x^{\prime}(t))^{\eta})^{\prime} \quad \text{and} \quad y(t)=a(t)(x^{\prime}(t))^{\eta}$ are considered. The approach taken here can be applied to other related fractional differential equations. Examples are provided to illustrate the relevance of the results obtained.
Access status: Open Access ,
On the global attractivity and the periodic character of a recursive sequence
(2010) Elsayed, E. M.
In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence $x_{n+1} = ax_n + \frac{bx_{n-1}+cx_{n+2}}{dx_{n-1}+ex_{n+2}}, \quad n=0,1,\ldots,$, where the parameters $a$, $b$, $c$, $d$ and $e$ are positive real numbers and the initial conditions $x_{-2}$, $x_{-1}$ and $x_{0}$ are positive real numbers.