Abstract: Fractional differential equations are more and more used to model the phenomena that usual differential equations can not model, since the traditional derivatives are local properties. At the same time the behavior of the solution is often determined not only by the nearby points, but by points in the whole domain and fractional derivatives present a way to capture it. In this talk we consider three problems related to fractional differential equations:

1). Discussion on derivation of a fractional conservation of mass equation from the first principles.

2). Fast numerical algorithm for the linear fractional advection-diffusion equations with nonlinear reaction term.

3). Approximate analytical solution to the time-fractional porous medium equation.

This is a joint work with Jeffrey Olsen, Anthony LaFleur, Emine Celik and Jeff Mortensen.