Fractional calculus is a 300 years topic, which has been introduced to real physics systems
modeling and engineering applications. In the last few decades, fractional-order nonlinear …

Fractional advection–dispersion equations (FADEs) have been widely used in hydrological
research to simulate the anomalous solute transport in surface and subsurface water …

This book explains the quantitative reasoning required by the fractional calculus applied to
complex physical, social, and biological phenomena. Fractional calculus is inextricably …

A new method that enables easy and convenient discretization of partial differential
equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays …

We study regularity for a parabolic problem with fractional diffusion in space and a fractional
time derivative. Our main result is a De Giorgi–Nash–Moser Hölder regularity theorem for …

In this paper, spatial diffusions are introduced to fractional-order coupled networks and the
problem of synchronization is investigated for fractional-order coupled neural networks with …

The continuous time random walk (CTRW) is a natural generalization of the Brownian
random walk that allows the incorporation of waiting time distributions ψ (t) and general …

In this work, we consider boundary value problems involving either Caputo or Riemann-
Liouville fractional derivatives of order $\alpha\in (1, 2) $ on the unit interval $(0, 1) $. These …

We present a numerical method for the Monte Carlo simulation of uncoupled continuous-
time random walks with a Lévy α-stable distribution of jumps in space and a Mittag-Leffler …

This study makes the first attempt to use the 2∕ 3-order fractional Laplacian modeling of
Kolmogorov− 5∕ 3 scaling of fully developed turbulence and enhanced diffusing …