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Browsing by Subject "integro-differential equations"

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    Item type:Article, 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.