English

Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation

Classical Analysis and ODEs 2007-05-23 v1 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.math/0110241,
  title  = {Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation},
  author = {Igor Podlubny},
  journal= {arXiv preprint arXiv:math/0110241},
  year   = {2007}
}

Comments

18 pages, 7 figures, 1 table