Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I was given this problem to challenge me

$$\frac{d^{1/2}}{dx^{1/2}}x^2 $$

I googled wikipedia, and tried to follow the steps shown.

I got an answer of $\frac{16\sqrt{ \pi x}}{9\pi}$ edited

2 part question.

a) is my answer correct? b) Reference request on a good paper/book on Fractional Calculus.

share|cite|improve this question
Your answer is wrong - just double check wikipedia to see the correct proof. There are plenty of references listed as well. – Bombyx mori Sep 19 '12 at 3:12
See example 2 at:… – Amzoti Sep 19 '12 at 3:42
up vote 14 down vote accepted

Related problem: (I), (II). Here is a formula where you can use it to find the fractional derivative of a monomial $x^n$,

$$ \frac{d^q}{dx^q} x^m = \frac{\Gamma(m+1)}{\Gamma(m-q+1 )} x^{m-q}\,. $$

The above formula was derived using the Riemann-Liouville definition for fractional derivative

$$ f^{(q)}(x) = \frac{1}{\Gamma(k-q)} \frac{d^k}{dx^k} \int_{a}^{x}\, (x-t)^{k-q-1}\,f(t)\,dt\>, \quad (k-1 < q < k )\,,$$ where $k=\lceil q \rceil$ is the ceiling of $q$.

See Chapter 2 in this book for details of derivation. In your case $q=\frac{1}{2}$, then the formula gives

$$ \frac{d^{\frac{1}{2}}}{dx^{\frac{1}{2}}} x^{2} = \frac{\Gamma(3)}{\Gamma(\frac{5}{2} )} x^{\frac{3}{2}} = \frac{8}{3 \sqrt{\pi}} x^{\frac{3}{2}}\,.$$

share|cite|improve this answer
@Michael: Thanks for the edit. – Mhenni Benghorbal May 30 '13 at 3:14

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.