Pasichnyk O. The Cauchy problem for time fractional diffusion equation in spaces of distributions

The Thesis is devoted to solvability of the Cauchy problem for diffusion equation with time fractional derivative in spaces of distributions of type D' and S'. The existence and uniqueness theorems and the representation by using the Green function of the solution of the Cauchy problem for linear diffusion equation with fractional time derivative and with distributions in the right-hand sides of an equation and initial condition have been obtained. The sufficient conditions for the solvability of the Cauchy problem for semi-linear equation of fractional diffusion with generalized function in the initial condition have been found.