4 papers
First-Passage Times for the Space-Fractional Spectral Fokker-Planck Equation
Christopher N. Angstmann, Daniel S. Han, Bruce I. Henry +1
We extend the random walk framework to include compounded steps, providing first-passage time (FPT) properties for a new class of superdiffusive processes, which are governed by th…
The Global Diffusion Limit for the Space Dependent Variable-Order Time-Fractional Diffusion Equation
Christopher N. Angstmann, Daniel S. Han, Bruce I. Henry +2
The diffusion equation and its time-fractional counterpart can be obtained via the diffusion limit of continuous time random walks with exponential and heavy-tailed waiting time di…
A compounded random walk for space-fractional diffusion on finite domains
Christopher N. Angstmann, Daniel S. Han, Bruce I. Henry +2
We formulate a compounded random walk that is physically well defined on both finite and infinite domains, and samples space-dependent forces throughout jumps. The governing evolut…
Finite Time Blowup of Integer- and Fractional-Order Time-Delayed Diffusion Equations
Christopher N. Angstmann, Stuart-James M. Burney, Daniel S. Han +3
In this work, exact solutions are derived for an integer- and fractional-order time-delayed diffusion equation with arbitrary initial conditions. The solutions are obtained using F…