  \noindent{\bf Abstract} We establish the long-time asymptotic formula of
solutions to the $(1+\alpha)$--order fractional differential equation
${}_{0}^{\>i}{\cal O}_{t}^{1+\alpha}x+a(t)x=0$, $t>0$, under some simple
restrictions on the functional coefficient $a(t)$, where ${}_{0}^{\>i}{\cal
O}_{t}^{1+\alpha}$ is one of the fractional differential operators
${}_{0}D_{t}^{\alpha}(x^{\prime})$,
$({}_{0}D_{t}^{\alpha}x)^{\prime}={}_{0}D_{t}^{1+\alpha}x$ and
${}_{0}D_{t}^{\alpha}(tx^{\prime}-x)$. Here, ${}_{0}D_{t}^{\alpha}$ designates
the Riemann-Liouville derivative of order $\alpha\in(0,1)$. The asymptotic
formula reads as $[a+O(1)]\cdot x_{{\scriptstyle small}}+b\cdot
x_{{\scriptstyle large}}$ as $t\rightarrow+\infty$ for given $a$,
$b\in\mathbb{R}$, where $x_{{\scriptstyle small}}$ and $x_{{\scriptstyle
large}}$ represent the eventually small and eventually large solutions that
generate the solution space of the fractional differential equation
${}_{0}^{\>i}{\cal O}_{t}^{1+\alpha}x=0$, $t>0$.
