2001/10/22 by Igor Podlubny
Mathematics · Physics and Astronomy · #math.CA #math-ph #math.MP #msc:26A33 #msc:26A42 #msc:83C99 #msc:44A35 #msc:45D05
published as Podlubny, I.: Geometric and physical interpretation of fractional integration and fractional differentiation. Fractional Calculus and Applied Analysis, vol. 5, no. 4, 2002, pp. 367--386. · 18 pages, 7 figures, 1 table
arxiv created 2001/10/22 · arxiv updated 2009/11/30
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.