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

Dmitriy M. Gordievskikh

Shadrinsk State Pedagogical University, K. Liebknecht Str., 3, Shadrinsk, Kurgan region, Russia

Abstract: 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.

Keywords and phrases: transition processes in semiconductors, fractional differential equation, caputo derivative, degenerate evolution equation, initial boundary value problem.

MSC: 39A45

Received: 01.09.2016

Language: English

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