Exact solutions to the fractional Boussinesq equation

FALCINI, FEDERICO; CERETANI, ANDREA N; GARRA, ROBERTO

Roma

Congreso; INdAM workshop: Fractional Differential Equations: Modeling, Discretization, and Numerical Solvers; 2021

We investigate the existence of exact solutions in closed form to a fractional version of the nonlinear Boussinesq equation for groundwater flow through an unconfined aquifer. We show this fractional equation appears naturally when the classical nonlinear Darcy’s law is replaced by a space-fractional one. After a physical discussion on the fractional model, we give several exact solutions in closed form for special choices of initial and boundary data. We provide solutions for steady andunsteady cases, by considering both classical and fractional derivatives in time.