Solvability of the boundary value problem for the equation of transition processes in semiconductors with a fractional time derivative

Necessary and sufficient conditions are established for the unique solvability of the initial boundary value problem for the equation describing the transition processes in semiconductors. The method of studying is the reducing to the Cauchy problem for a degenerate evolution equation of fractional order in a Banach space. Using the functional calculus in the Banach algebra of bounded linear operators a form of the considered problem solution is performed.