We derive an integro-differential equation for the joint probability density function in phase space associated with the continuous-time random walk, with generic waiting time probability density function and external force. This equation permits us to investigate whole diffusion processes...

The purpose of this paper is to offer a unified discussion of variable-order differential operators in anomalous diffusion modeling. The characteristics of the new models, in contrast to constant-order fractional diffusion models, change with time, space, concentration or other independent...