Linking fractional calculus to real data

Paradisi P.

Stochastic processes  Renewal processes  Fractional calculus  Anomalous diffusion  Time series analysis 

I will review some well-known theoretical findings about fractional calculus and, in particular, the links between fractal intermittency, the Continuous Time Random Walk (CTRW) model and the emergence of Fractional Diffu- sion Equations (FDE) for anomalous diffusion. In this framework, I will show how fractional operators are associated with the existence of renewal events, a typical feature of complex systems. I will also discuss the possibile connections with critical phenomena. Then, I will introduce some statistical methods allowing to understand when a real system could be described by means of fractional models. Finally, I will show some applications to real data from nano-crystal fluores- cence intermittency, human brain dynamics and atmospheric turbulence.

Source: FCPNLO 2014 - Fractional Calculus, Probability and Non-local Operators: Applications and Recent Developments. A workshop on the occasion of the retirement of Francesco Mainardi, Bilbao, Spain, 6-8 November 2013