This paper reviews some applications of continuous time random walks (CTRWs) to Finance
and Economics. It is divided into two parts. The first part deals with the connection between …

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 …

Fractional advection–dispersion equations are used in groundwater hydrology to model the
transport of passive tracers carried by fluid flow in a porous medium. In this paper we …

Nonlocal and fractional-order models capture effects that classical partial differential
equations cannot describe; for this reason, they are suitable for a broad class of engineering …

Fractional diffusion equations model phenomena exhibiting anomalous diffusion that can
not be modeled accurately by the second-order diffusion equations. Because of the nonlocal …

Fractional order partial differential equations, as generalizations of classical integer order
partial differential equations, are increasingly used to model problems in fluid flow, finance …

Spatially fractional order diffusion equations are generalizations of classical diffusion
equations which are used in modeling practical superdiffusive problems in fluid flow, finance …

Continuous time random walks (CTRWs) are used in physics to model anomalous diffusion,
by incorporating a random waiting time between particle jumps. In finance, the particle …

A continuous time random walk (CTRW) is a random walk subordinated to a renewal
process, used in physics to model anomalous diffusion. Transition densities of CTRW …

We develop the basic tools of fractional vector calculus including a fractional derivative
version of the gradient, divergence, and curl, and a fractional divergence theorem and …