The fractional Laplacian in R d, which we write as (− Δ) α/2 with α∈(0, 2), has multiple
equivalent characterizations. Moreover, in bounded domains, boundary conditions must be …

A Review of Definitions for Fractional Derivatives and Integral Page 1 See discussions, stats,
and author profiles for this publication at: https://www.researchgate.net/publication/275071882 …

This handbook covers the peridynamic modeling of failure and damage. Peridynamics is a
reformulation of continuum mechanics based on integration of interactions rather than …

Fractional calculus is a rapidly growing field of research, at the interface between probability,
differential equations, and mathematical physics. It is used to model anomalous diffusion, in …

A recently developed nonlocal vector calculus is exploited to provide a variational analysis
for a general class of nonlocal diffusion problems described by a linear integral equation on …

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the
two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed …

Fractional differential equations are becoming increasingly used as a powerful modelling
approach for understanding the many aspects of nonlocality and spatial heterogeneity …

Книга содержит изложение метода дробных производных и состоит из трех частей,
раскрывающих физические основания метода, математический аппарат и примеры …

We describe the most important developments in the application of three theoretical tools to
modeling of the morphology of porous media and flow and transport processes in them. One …

Characterizing the collective behavior of particle transport on the Earth surface is a key
ingredient in describing landscape evolution. We seek equations that capture essential …