Application of fractional calculus to fractal media

Research output: Chapter in Book/Report/Conference proceedingChapter


This chapter is a survey of continuum-type mechanics of porous media having a generally anisotropic fractal geometry. The approach relies on expressing the global balance laws in terms of fractional integrals based on product measures and, then, converting them to integer-order integrals in conventional (Euclidean) space. Via localization, this allows development of local balance laws of fractal media: conservation of mass, microinertia, linear momentum, angular momentum, and energy; also the second law of thermodynamics. The product measure formulation, together with the angular momentum balance, directly leads to a generally asymmetric Cauchy stress and, hence, to a micropolar (rather than classical) mechanics of fractal materials. The continuum-thermodynamic development follows the lines of thermomechanics with internal variables.

Original languageEnglish (US)
Title of host publicationApplications in Physics, Part A
PublisherDe Gruyter
Number of pages14
ISBN (Electronic)9783110571707
ISBN (Print)9783110570885
StatePublished - Jan 1 2019


  • Anisotropic fractals
  • Balance laws
  • Continuum mechanics
  • Micropolar continuum
  • Product measure

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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