Let us now consider the Fokker-Planck equation, which is a partial differential equation that
describes the time evolution of the PDF of the positions of particles, and was introduced in …

We derive, through subordination techniques, a generalized Feynman–Kac equation in the
form of a time fractional Schrödinger equation. We relate such equation to a functional which …

The bilateral tempered fractional derivatives are introduced generalising previous works on
the one-sided tempered fractional derivatives and the two-sided fractional derivatives. An …

In this paper, we are concerned with the numerical solution for the backward fractional
Feynman–Kac equation with non-smooth initial data. Here we first provide the regularity …

In the beginning of this book, we will introduce some fundamental concepts of probability
theory which is the basis of describing the anomalous and nonergodic processes in the …

This book investigates statistical observables for anomalous and nonergodic dynamics,
focusing on the dynamical behaviors of particles modelled by non-Brownian stochastic …

This paper provides a finite difference discretization for the backward Feynman–Kac
equation, governing the distribution of functionals of the path for a particle undergoing both …

Diffusion is a ubiquitous transport mechanism across countless natural and synthetic
systems. In many of these systems the spatial domain is not homogeneous and often …