The standard central limit theorem plays a fundamental role in Boltzmann-Gibbs statistical
mechanics. This important physical theory has been generalized 1 in 1988 by using the …

We obtain the integration by parts formula for the regional fractional Laplacian which are
generators of symmetric α-stable processes on a subset of R^ n (0< α< 2). In this formula, a …

This research monograph is motivated by problems in mathematical physics that involve
fractional kinetic equations. These equations describe transport dynamics in complex …

In this paper diffusion processes with changing modes are studied involving the variable
order partial differential equations. We prove the existence and uniqueness theorem of a …

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 …

The book is devoted to the mathematical foundations of nonextensive statistical mechanics.
This is the first book containing the systematic presentation of the mathematical theory and …

We treat the question of existence, uniqueness and construction of a solution to the Cauchy
and multi-point problems for a general linear evolution equation with (in general) temporal …

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 …

We investigate a class of semilinear parabolic and elliptic problems with fractional dynamic
boundary conditions. We introduce two new operators, the so-called fractional Wentzell …

It is known that the transition probabilities of a solution to a classical Itô stochastic differential
equation (SDE) satisfy in the weak sense the associated Kolmogorov equation. The …