A Fokker-Plank equation with a fractional derivative along the trajectory of motion with conservation law.

The paper presents a new mathematical model of the convection-diffusion process with 'memory along the flow path'. It is described by one-dimensional initial-boundary value problem with a fractional derivative along the characteristic curve of convection operator. The constructed model satisfies the local and global conservation laws. The finite-difference approximation of the problem is constructed on the base of Lagrange approach. The stability and discrete conservation laws are proven for algorithmic realization of this approximation. [ABSTRACT FROM AUTHOR]