A physical approach to the connection between fractal geometry and fractional calculus

Salvatore Butera, Mario Di Paola

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

Our goal is to prove the existence of a connection between fractal geometries and fractional calculus. We show that such a connection exists and has to be sought in the physical origins of the power laws ruling the evolution of most of the natural phenomena, and that are the characteristic feature of fractional differential operators. We show, with the aid of a relevant example, that a power law comes up every time we deal with physical phenomena occurring on a underlying fractal geometry. The order of the power law depends on the anomalous dimension of the geometry, and on the mathematical model used to describe the physics. In the assumption of linear regime, by taking advantage of the Boltzmann superposition principle, a differential equation of not integer order is found, ruling the evolution of the phenomenon at hand.

Original languageEnglish
Title of host publication2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014
PublisherIEEE
ISBN (Print)9781479925919
DOIs
Publication statusPublished - 2014
Event2014 International Conference on Fractional Differentiation and Its Applications - Catania, United Kingdom
Duration: 23 Jun 201425 Jun 2014

Conference

Conference2014 International Conference on Fractional Differentiation and Its Applications
Abbreviated titleICFDA 2014
CountryUnited Kingdom
CityCatania
Period23/06/1425/06/14

Fingerprint Dive into the research topics of 'A physical approach to the connection between fractal geometry and fractional calculus'. Together they form a unique fingerprint.

Cite this