Discussion Overview
The discussion revolves around the various definitions of fractional derivatives, specifically questioning the equivalence of these definitions, including the Riemann-Liouville differintegral, Grunwald-Letnikov derivative, Hadamard, and Caputo derivatives. The scope includes theoretical aspects of fractional calculus.
Discussion Character
Main Points Raised
- One participant asks about the number of definitions for fractional derivatives beyond the Riemann-Liouville differintegral and whether they are all equivalent.
- Another participant mentions the Grunwald-Letnikov derivative and asserts that all definitions are equivalent, suggesting that having multiple definitions for the same concept is pointless.
- A different viewpoint argues that having multiple definitions is not pointless but indicates inconsistency among them.
- One participant introduces the Hadamard and Caputo derivatives and requests links to their definitions, expressing a concern about the complexity of the Riemann-Liouville differintegral when calculating integer derivatives.
Areas of Agreement / Disagreement
Participants express disagreement regarding the equivalence of the various definitions of fractional derivatives, with some asserting equivalence while others highlight inconsistencies.
Contextual Notes
There are unresolved questions regarding the assumptions underlying the definitions and their applicability, as well as the implications of using different definitions in practice.