Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.
Please help promote PhysicsOverflow ads elsewhere if you like it.
PO is now at the Physics Department of Bielefeld University!
New printer friendly PO pages!
Migration to Bielefeld University was successful!
Please vote for this year's PhysicsOverflow ads!
Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!
... see more
(propose a free ad)
I define the fractional q-derivation:
Dαq(f)(x)=[(f(qx)−f(x))/((q−1)x)]α=
=1((1−q)x)α∞∑n=0(−1)n[(1−qCαn)/(1−q)]f(qnx)q−n
We have:
Dαq∘Dβq=Dα+βq
DαqT=qαTDαq
with T(f)(x)=f(qx).
Have we algebraic properties of the fractional q-derivations?
Is it a fractional derivative? What is fractional in it? There is no limit process like ε→0 in your first formula, so it is an expression rather than a derivative of any kind.
"Have we algebraic properties of the fractional q-derivations?"
What sort of question is this?
Most expressions have algebraic properties. The relations you provide for your D-operator are algebraic properties.
So what?
Are you asking for further algebraic properties? If the "fractional q-derivation" is indeed your definition, it would seem you are the person first called upon to work these out.
The formula I proposed is false but it is plausible and you can consult arxiv.org for the good definition of the fractional q-derivative.
As I remarked on a previous occasion, you maybe should put more care in your questions.
Furthermore, I suppose that the sources on arxiv.org to be consulted "for the good definition" contain also algebraic properties of the respective fractional q-derivative.
user contributions licensed under cc by-sa 3.0 with attribution required