FRACTIONAL CALCULUS PROJECT

Partially supported by research grants DMS-0139943, DMS-0139927, DMS-0417972 and DMS-0417869 from the USA National Science Foundation, and the Marsden Foundation in New Zealand.

The Fractional Calculus Project is an interdisciplinary collaboration of mathematicians, statisticians, physicists and hydrologists to develop the theory and practical application of fractals, fractional derivatives, and heavy tailed stochastic processes.

Fractional-order partial differential equations (PDEs) are used by physicists and hydrologists to model anomalous diffusion and Hamiltonian chaos.  These governing equations describe the asymptotic behavior of continuous time random walks (CTRWs).  Stochastic solutions to the simplest governing equations are Levy motions, generalizing the Brownian motion solution to the classical diffusion equation.  More generally, these equations invoke pseudo-differential operators that are non-local.  Fractional PDEs address shortcomings with previous methods in geophysics, but a number of important problems remain open.

Senior investigators:

Inmaculada B. Aban, Department of Biostatistics, School of Public Health, The University of Alabama at Birmingham.
Boris Baeumer, Department of Mathematics & Statistics, University of Otago, Dunedin, New Zealand.
David A. Benson, Department of Geology and Geological Engineering, Colorado School of Mines
Tomasz J. Kozubowski, Department of Mathematics & Statistics, University of Nevada, Reno.
Mark M. Meerschaert, Department of Mathematics & Statistics, University of Otago, Dunedin, New Zealand.
Jeff Mortensen, Department of Mathematics & Statistics, University of Nevada, Reno.
Anna K. Panorska, Department of Mathematics & Statistics, University of Nevada, Reno.
Hans-Peter Scheffler, Department of Mathematics, University of Siegen, Germany.
Stephen W. Wheatcraft, Department of Geological Sciences, University of Nevada, Reno.

Postdoctoral and graduate students:

Mihaly Kovacs, Postdoctoral Research Assistant, Department of Mathematics & Statistics, University of Otago, Dunedin, New Zealand.
Matt Reeves, graduate student, Program in Hydrologic Sciences,  University of Nevada, Reno.
Charles Tadjeran, Postdoctoral Research Assistant, Department of Mathematics & Statistics, University of Nevada, Reno.
Yong Zhang, Postdoctoral Research Assistant, Department of Geology and Geological Engineering, Colorado School of Mines.

Other researchers affiliated with the Fractal Calculus Project:

Peter Becker-Kern, Department of Mathematics, University of Dortmund, Germany.
Rina Schumer, Desert Research Institute, Reno, Nevada.

From left to right...
Back row:  Steve, Boris, Rina (expecting Maia), Charles holding Joseph (son of Tom and Ania)
Middle row:  Dave
Front row:  Tom, Ania, Mark

Mark (left) and Boris discuss some new research in New Zealand.

PREPRINTS:  You can download the latest results from the web pages of Mark M. Meerschaert and David A. Benson.