A high-order L2 type difference scheme for the time-fractional diffusion equation

The present paper is devoted to constructing L2 type difference analog of the Caputo fractional derivative. fundamental features this operator are studied and it used construct schemes generating approximations second fourth order in space (3−α)th-order time for diffusion equation with variable coefficients. Difference were also constructed variable-order generalized fractional-order Sobolev type. Stability under consideration as well their convergence rate equal approximation error proven. received results supported by numerical computations performed some test problems.