Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation
Podlubny, Igor
arXiv, 0110241 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2001-10-22
Classification:  Mathematics - Classical Analysis and ODEs,  Mathematical Physics,  26A33 (Primary) 26A42, 83C99, 44A35, 45D05 (Secondary) 
@article{0110241,
     author = {Podlubny, Igor},
     title = {Geometric and Physical Interpretation of Fractional Integration and
  Fractional Differentiation},
     journal = {arXiv},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0110241}
}

Podlubny, Igor. Geometric and Physical Interpretation of Fractional Integration and
  Fractional Differentiation. arXiv, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/0110241/