Abstract
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.
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