I would like to understand if it is possible to completely characterize real-valued functions with an expansion of this type:
$f(x)=f'(0)\cdot x + o(x^{\alpha})\qquad \alpha \in (1,2)$
I am not familiar with fractional calculus, so even though the question seems reasonable I have troubles finding references.
Thanks to anyone who can point me out in the right direction!