Closed form of the Solutions of some Boundary-Value Problems for Anomalous Diffusion Equation with Hilfer’s Generalized Derivative

The concept of double-order fractional derivative generalizing the well-known Hilfer’s derivative is introduced. The formula is given for the Laplace transform of double-order fractional derivative, which is used to solve the Cauchy-type problem for equations of fractional order with this derivative. The closed solutions to some boundary-value problems for the equation of anomalous diffusion with double-order fractional derivative in time are obtained.