Suppose we have a fractional differential equation: $$\left[D^{nv}+a_{1}D^{\left(n-1\right)v}+\dots+a_{n}D^{0}\right]y(t)=0$$ where $\nu=\frac{1}{q}$ and $q\in\mathbb{N}$ and y is an analytic function.
How can we prove that the kernel of the differential operator $$\left[D^{nv}+a_{1}D^{\left(n-1\right)v}+\dots+a_{n}D^{0}\right]$$ has dimension $N=\lceil{n\nu}\rceil$?
Thanks a lot.