  We estimate the growth in time of the solutions to a class of nonlinear
fractional differential equations $D_{0+}^{\alpha}(x-x_0) =f(t,x)$ which
includes $D_{0+}^{\alpha}(x-x_0) =H(t)x^{\lambda}$ with $\lambda\in(0,1)$ for
the case of slowly-decaying coefficients $H$. The proof is based on the triple
interpolation inequality on the real line and the growth estimate reads as
$x(t)=o(t^{a\alpha})$ when $t\to+\infty$ for $1>\alpha>1-a>\lambda>0$. Our
result can be thought of as a non--integer counterpart of the classical Bihari
asymptotic integration result for nonlinear ordinary differential equations. By
a carefully designed example we show that in some circumstances such an
estimate is optimal.
