A fractional hydro-dynamic model for network supervision

The study proposed in this paper is part of a larger scientific collaboration involving a large academic community, and it is specifically focused on the modeling aspects of advection–diffusion problems in water monitoring and distribution systems. The main idea proposed in this work is the study of an anomalous advection–diffusion process for water distribution systems. Indeed, the dynamics of water within distribution systems is characterized by different velocity regimes, ranging from laminar, transitional and turbulent, which lead to an advective and diffusive-dispersive behavior of the contaminant spread. This phenomenon, usually modeled by a classical advection-dispersion-reaction equation, through the introduction of a fractional derivative operator, will be modeled by a new fractional model, of advection-dispersion-reaction equation, which allows to describe anomalous processes. The fractional model has been studied numerically, attempting the fitting real phenomena.