Timeline for Why are there so many fractional derivatives?
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| Oct 14, 2021 at 20:56 | comment | added | Tom Copeland | Yes, ops are ill-defined if what they are operating on, and how, are not well-defined. One of the most productive definitions of a fractional integro-derivative calculus, with an axiomatic approach given by Pincherle, is that of Heaviside, which I sketch in mathoverflow.net/questions/381566/… and various linked MO and MSE posts. This is closely related to the Riemann-Liouville fractional calculus and the theory of distributions/generalized functions as well as older classical math and physics. | |
| Nov 7, 2017 at 2:15 | comment | added | Terry Tao | If one views ordinary and fractional derivatives as densely defined operators on function spaces, then there are almost as many ordinary derivatives as fractional derivatives, as one can vary the function space or norm, alter the domain, impose boundary conditions, etc.. The difference is that all the different possibilities for ordinary differentiation coincide when working locally with nice functions away from boundaries, which is not the case for fractional differentiation. (Also branch cuts can yield some additional variability for fractional derivatives compared with ordinary ones.) | |
| Nov 4, 2017 at 16:23 | vote | accept | FusRoDah | ||
| Nov 4, 2017 at 9:57 | history | answered | coudy | CC BY-SA 3.0 |