Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation

Details Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation

2001-10-22

arxiv.org/abs/math/0110241v1

Podlubny, I.: Geometric and physical interpretation of fractional integration and fractional differentiation. Fractional Calcu

Mathematics

Classical Analysis and ODEs

18 pages, 7 figures, 1 table

Scientific paper

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.

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