Fractional Advection-Diffusion Equation for Water Distribution Systems

In this paper the fractional advection-diffusion equation is analysed with the aim of describing the behavior of water distribution systems. The model is defined by means of a Fractional Partial Differential Equation, that is, first of all, reduced to an Ordinary Differential Equation and, then, numerically solved. An integration scheme for the initial value problem, based on Finite Difference Scheme, is proposed and applied to appropriate choices for model parameters as well as for the source term. The main idea is to investigate the role of the fractional derivative with reference to realistic problems, such as contaminant transport mechanism in water distribution systems.