Boundary value problems for the diffusion equation of the variable order   in differential and difference settings
  Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori estimates for these problems exactly as in the classical case. The credibility of the obtained results is verified by performing numerical calculations for a test problem. 
A. A. Alikhanov
math.NA math-ph math.MP