Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader
area of fractional calculus that has important and far-reaching applications for the modeling …

We consider anomalous stochastic processes based on the renewal continuous time
random walk model with different forms for the probability density of waiting times between …

Mittag-Leffler Functions, Related Topics and Applications Page 1 Springer Monographs in
Mathematics Rudolf Gorenflo Anatoly A. Kilbas Francesco Mainardi Sergei Rogosin Mittag-Leffler …

The twentieth century was rich in great scientific discoveries. One of the most influential
events is the introduction of diffusion process, which has been widely used in physics …

The book is devoted to the fundamental relationship between three objects: a stochastic
process, stochastic differential equations driven by that process and their associated Fokker …

This book is an unique integrated treatise, on the concepts of fractional calculus as models
with applications in hydrology, soil science and geomechanics. The models are primarily …

The classical Duhamel principle, established nearly 200 years ago by Jean-Marie-Constant
Duhamel, reduces the Cauchy problem for an inhomogeneous partial differential equation to …

This survey describes the method of approximation of operator semigroups, based on the
Chernoff theorem. We outline recent results in this domain as well as clarify relations …

This paper presents mass-time fractional partial differential equations (fPDEs) formulated in
a material coordinate for swelling–shrinking soils, and space-time fPDEs formulated in …

We consider simulation of spatially one-dimensional space-time fractional diffusion.
Whereas in an earlier paper of ours we have developed the basic theory of what we call …