We investigate the spatiotemporal nonlocality underlying fractional-derivative models as a
possible explanation for regional-scale anomalous dispersion with heavy tails. Properties of …

The inverse stable subordinator provides a probability model for time-fractional differential
equations, and leads to explicit solution formulae. This paper reviews properties of the …

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an
exponential factor leads to tempered fractional derivatives and integrals. Tempered …

We develop a kind of fractional calculus and theory of relaxation and diffusion equations
associated with operators in the time variable, of the form (\mathbb D_ (k) u)(t)= d dt …

Passive tracers in heterogeneous media experience preasymptotic transport with scale‐
dependent anomalous diffusion, before eventually converging to the asymptotic diffusion …

The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its
distributions solve a time-fractional analogue of the Kolmogorov forward equation for a …

We extend the particle-tracking method to simulate general multi-rate mass transfer (MRMT)
equations. Previous methods for single-rate equations used two-state Markov chains and …

In this paper, we study the existence and uniqueness of solutions for general fractional-time
parabolic equations of mixture type, and their probabilistic representations in terms of the …

Fractional derivatives can be used to model time delays in a diffusion process. When the
order of the fractional derivative is distributed over the unit interval, it is useful for modeling a …

This paper takes under consideration subordinators and their inverse processes (hitting-
times). The governing equations of such processes are presented by means of convolution …