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 …

Fractional Cauchy problems replace the usual first-order time derivative by a fractional
derivative. This paper develops classical solutions and stochastic analogues for fractional …

The present work provides a critical assessment of numerical solutions of the space-
fractional diffusion-advection equation, which is of high significance for applications in …

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 …

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 …

It is shown that under a certain condition on a semimartingale and a time-change, any
stochastic integral driven by the time-changed semimartingale is a time-changed stochastic …

In this paper Fokker-Planck-Kolmogorov type equations associated with stochastic
differential equations driven by a time-changed fractional Brownian motion are derived. Two …

We present the stochastic solution to a generalized fractional partial differential equation
(fPDE) involving a regularized operator related to the so-called Prabhakar operator and …

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 …