Shadows on the walls: Geometric interpretation of fractional integration

Igor Podlubny*, Vladimir Despotovic, Tomas Skovranek, Brandon H. McNaughton

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

11 Citations (Scopus)


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.

Original languageEnglish
JournalJournal of Online Mathematics and its Applications
Publication statusPublished - Nov 2007
Externally publishedYes


  • Fractional calculus
  • Fractional integral
  • Geometric interpretation


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