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


This paper is concerned with the asymptotic behavior of nonoscillatory
solutions of forced fractional differential equations of the form
^{C}D_{c}^{\alpha }y(t)=e(t)+f(t,x(t)), \quad c>1,\quad \alpha \in (0,1),
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.