You are here

Shadows on the Walls: Geometric Interpretation of Fractional Integration

Author(s): 
Igor Podlubny, Vladimir Despotovic, Tomas Skovranek and Brandon H. McNaughton

Abstract

In 2001/2002, Podlubny suggested a solution to the more than 300-years old problem of geometric interpretation of fractional integration (i.e., integration of an arbitrary real order). His geometric interpretation for left-sided and right-sided Riemann-Liouville fractional integrals, and for Riesz potential is given in terms of changing time scale with constant order of integration, and also in a case of varying order of integration with constant time parameter. In this article we present animations of such interpretation.

Technologies Used in This Article

This article uses several animated GIF images that are displayed with JavaScript. You will need a browser that supports JavaScript, and you will need JavaScript enabled.

This article also uses the following HTML symbols: α (alpha), τ (tau). If these do not display properly, you may need to update your browser.

Keywords

  • fractional calculus
  • fractional integral
  • geometric interpretation

Publication data

  • Published November, 2007; article ID 1664
  • Copyright © 2007, by Igor Podlubny, Vladimir Despotovic, Tomas Skovranek, and Brandon H. McNaughton

Article Link

Igor Podlubny, Vladimir Despotovic, Tomas Skovranek and Brandon H. McNaughton, "Shadows on the Walls: Geometric Interpretation of Fractional Integration," Convergence (November 2007)