The cable model is widely used in several fields of science to describe the propagation of signals. A relevant medical and biological example is the anomalous subdiffusion in spiny neuronal dendrites observed in several studies of the last decade. Anomalous subdiffusion can be modelled in several ways introducing some fractional component into the classical cable model. The Chauchy problem asso...

the performance of water flooding can be investigated by using either detail numerical modeling or simulation, or simply through the analytical buckley-leverett (bl) model. the buckley-leverett analytical technique can be applied to one-dimensional homogeneous systems. in this paper, the impact of heterogeneity on water flooding performance and fractional flow curve is investigated. first, a ba...

We prove well-posedness and regularity of solutions to a fractional diffusion porous media equation with variable order that may depend on the unknown solution. present linearly implicit time-stepping method linearize discretize in time, rigorous analysis for convergence numerical based proved results.

{ Fractional calculus allows to generalize the standard (linear and one dimensional) diiusion equation by replacing the second-order space derivative by a derivative of fractional order. If this is taken as the pseudo-diierential operator introduced by Feller in 1952 the fundamental solution of the resulting diiusion equation is a probability density evolving in time and stable in the sense of ...