M M Meerschaert

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However,...

Karamata's Tauberian theorem relates the asymptotics of a nondecreasing right-continuous function to that of its Laplace-Stieltjes transform, using regular variation. This paper establishes the analogous Tauberian theorem for matrix-valued functions....

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2),...

Extension of the fractional diffusion equation to two or three dimensions is not as simple as extension of the second-order equation. This is revealed by the solutions of the equations:...

The long-term limit motions of individual heavy-tailed (power-law) particle jumps that characterize anomalous diffusion may have different scaling rates in different directions. Operator stable motions [Y(t):t> or =0] are limits...

A fractional advection-dispersion equation (ADE) is a generalization of the classical ADE in which the second-order derivative is replaced with a fractional-order derivative. In contrast to the classical ADE, the...