A class of time-fractional diffusion equations with generalized fractional derivatives

Abstract

In this paper, we consider generalized fractional derivatives, which are characterized by a scale function and a weight function. It is proposed to replace the time variable with a new variable, associated with the scale and weight functions, which allows us to reduce the problems for equations with generalized fractional derivatives to problems for equations with the usual fractional derivative. The equations obtained after the above change of variables are quite well studied, so that one can apply well-known effective numerical methods and use the reverse substitution to find solutions to the original problems.