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.
|Title of host publication||2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014|
|Publication status||Published - 2014|
|Event||2014 International Conference on Fractional Differentiation and Its Applications - Catania, United Kingdom|
Duration: 23 Jun 2014 → 25 Jun 2014
|Conference||2014 International Conference on Fractional Differentiation and Its Applications|
|Abbreviated title||ICFDA 2014|
|Period||23/06/14 → 25/06/14|