Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation
Abstract
A solution to the more than 300years 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 RiemannLiouville 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 eprints
 Pub Date:
 October 2001
 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)
 EPrint:
 18 pages, 7 figures, 1 table