Talk by Dr. Marianito Rodrigo (DSAS colloquium)

Title: Revisiting the fractional order diffusion and wave equations

Abstract:
The diffusion (or heat) equation is first order in time, while the wave
equation is second order in time. When we interpolate through time
derivatives of arbitrary order, such as the Riemann-Liouville and Caputo
fractional derivatives, then we obtain a so-called fractional order
diffusion-wave equation. Can we obtain analogous expressions for the
associated initial value problems? I will give a whirlwind tour of the
fractional calculus and look at the solutions of these initial value
problems. I will also briefly discuss how the fractional order diffusion
equation gives rise to non-Gaussian probability distributions.