How can one define a fractional-order derivative of a vector?

Question

I am not familiar much with fractional-order derivatives, for instance, if $\mathbf{x}\in\mathbf{R}^{n}$, then how can one define: $$ D^{q-1}\mathbf{x}\quad\text{and}\quad D^{q}\mathbf{x}?\tag{1} $$ I hope someone can suggest a more analytic expression for $(1)$