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Questions regarding derivatives and integrals of non-integer order.

5 votes

Fourier transform of fractional differential operator and Plancherel formula equivalent for ...

I'd like to add a little bit to the answers by Dick Palais and Denis Serre. The standard way to define a fractional derivative of order $\alpha>0$ on the real axis is via the Riemann-Liouville integr …
Andrey Rekalo's user avatar
52 votes
Accepted

Geometric interpretation of the half-derivative?

A possible mechanical interpretation of the half-derivative can be given in terms of Abel's solution to a classical problem from the calculus of variations (the tautochrone problem). Let there be a …
Andrey Rekalo's user avatar