December 2001 - 011203
A Pre-Print on the possible Geometric and Physical Interpretations of Fractional Calculus by I. Podlubny

math.CA/0110241   [ link ]

Title: Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation
Authors: Igor Podlubny
Subj-class: Classical Analysis; General Mathematics; Mathematical Physics

A solution to the more than 300-years old problem of geometric and physical interpretation of fractional integration and differentiation (i.e., integration and differentiation of an arbitrary real order) is suggested for the Riemann-Liouville fractional integration and differentiation, the Caputo fractional differentiation, the Riesz potential, and the Feller potential. It is also generalized for giving a new geometric and physical interpretation of more general convolution integrals of the Volterra type.
Besides this, a new physical interpretation is suggested for the Stieltjes integral.