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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.

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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

JOMA

Journal of Online Mathematics and its Applications

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