On the Asymptotic Behavior of Solutions of Certain Forced Fractional Differential Equations

Abstract

This paper is concerned with the asymptotic behavior of nonoscillatory
solutions of forced fractional differential equations of the form
\begin{equation*}
^{C}D_{c}^{\alpha }y(t)=e(t)+f(t,x(t)), \quad c>1,\quad \alpha \in (0,1),
\end{equation*}
where $y(t) = x^{\prime \prime \prime}(t)$, $c_{0}=\frac{y(c)}{\Gamma
(1)}=y(c)$, and $c_{0}$ is a real constant. In obtaining their results,
the authors develop a technique that can be applied to some
related fractional differential equations with Caputo derivatives of
any order. An example is also provided to illustrate the results.