Dirichlet Problems for Mixed-Type Equations with Fractional Derivatives

Abstract In this paper, we study the first boundary value problem for mixed-type equations with fractional derivatives in rectangular domains. A uniqueness criterion for the solution of the problem is established. The solution is constructed as a sum of an orthogonal series and its convergence is shown in the class of regular solutions of these equations. The stability of the solution with respect to given boundary functions is established in the class of continuous and square-summable functions.

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