Definitions of Fractional derivative

[Klaus_Hoffmann]

how many definitions appart from the 'Riemann-Liouville differintegral' to define the fractional derivative of f(x) or $$x^{a}f(x)$$ for real or complex 'a' are them all equivalents??

 

[Gib Z]

The other variation is the Grunwald-Letnikov Derivative, and all definitions are equivalent. It's pretty pointless if you have 2 different definitions for the same thing..

 

[MathematicalPhysicist]

not pointless, but inconsistent.

 

[Klaus_Hoffmann]

I heard also about Hadamard and Caputo derivatives for fractional calculus could anyone give a link with the definition?

a great inconvenient i see to Riemann-Liouville differintegral is the fact that for an integer m you must calculate expression $$\frac{d^{m}}{dx^{m}}$$