'Fractional Calculus I' !

Orion1

I have located a paper claiming that it is possible to fractionally differentiate, called 'Fractional Calculus I'

Orion1 derivative integer factorial theorem:
$$\frac{d^n}{dx^n} (x^n) = n!$$

Is this paper correct? is 'Fractional Calculus' really possible?

Fractional Integration?

Reference:
https://www.physicsforums.com/showpost.php?p=672326&postcount=1

Last edited:

Staff Emeritus
Gold Member
Yep! It's not nearly as nice as ordinary calculus, but you can still do it, and can apparently do cool stuff with it.

Homework Helper
Fractional (and real and complex) order operators are possible and are used. Unfortunately several results that one might expect do not hold. For example
(D^n)exp(a x)=(a^n)exp(a x)
and
(D^n)cos(a x)=(a^n)cos(a x+n pi/2)
do not hold in fractional calculus.

deepurple
Yes fractional calculus is really useful tool for modeling problems in physics, biology and engineering. Actually fractional difference calculus is possible also.

Gold Member
How does one perform a fractional derivative on a transcendental function? Although it seems quite trivial on algebraic functions.

The first time the idea of fractional calculus occurred to me, not knowing it was a real thing, was when I was thinking about how to calculate, in quantum mechanics, something like $<\psi |\hat{p}^n |\psi>$ where $\hat{p}=-i\hbar \frac{d}{dx}$. I was indeed quite surprised to find that fractional calculus was a real thing.