Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation
Abstract
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- October 2001
- DOI:
- 10.48550/arXiv.math/0110241
- arXiv:
- arXiv:math/0110241
- Bibcode:
- 2001math.....10241P
- Keywords:
-
- Mathematics - Classical Analysis and ODEs;
- Mathematical Physics;
- Mathematics - Mathematical Physics;
- 26A33 (Primary) 26A42;
- 83C99;
- 44A35;
- 45D05 (Secondary)
- E-Print:
- 18 pages, 7 figures, 1 table