Abstract:
The first initial boundary value problem for a loaded differential equation of fractional order convection diffusion is considered. A difference scheme approximating this problem is constructed on a uniform grid. To solve the problem, assuming the existence of a regular solution, a priori estimates in differential and difference forms are obtained. From these estimates follow the uniqueness and continuous dependence of the solution on the input data of the problem, as well as the convergence with the rate $O(h^2+\tau^2)$.
Keywords:loaded equations, boundary value problems, a priori estimation, convection diffusion equation, fractional order differential equation, fractional Caputo derivative.
Fulltext:
PDF file (387 kB)