MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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

It is well known that in the case of integer order differentiation the formula $\partial_{x}f(x,u(x))=\partial_{u}f\cdot \partial_{x}u+\partial_{x}f\cdot u$ holds. If we define fractional derivative via Fourier transform F as $D_{x}^{\alpha}u(x)=F^{-1}[{(i\xi)^{\alpha}\widehat{u}(\xi)}]$, where ^ denotes the Fourier transform, is there a similarly formula for $D_{x}^{\alpha}f(x,u(x))$?

share|cite|improve this question
The fractional derivative is of order 0<\alpha<1 – Milos Sep 19 '13 at 8:06
1 – Carlo Beenakker Sep 19 '13 at 20:44

If you are interested in estimates (rather than pointwise equalities), you might check out this paper of Christ and Weinstein:

See in particular Proposition 3.1 therein.

share|cite|improve this answer

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.