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Dirichlet Problems for Mixed-Type Equations with Fractional Derivatives

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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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Authors and Affiliations

  1. Institute of Mathematics with Computing Centre—Subdivision of the Ufa Federal Research Center of Russian Academy of Sciences, 450008, Ufa, Russia

    K. B. Sabitov

  2. Sterlitamak Branch, Bashkir State University, 453126, Sterlitamak, Russia

    K. B. Sabitov

Authors
  1. K. B. Sabitov
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Correspondence to K. B. Sabitov.

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Translated by A. Muravnik

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Sabitov, K.B. Dirichlet Problems for Mixed-Type Equations with Fractional Derivatives. Russ Math. 66, 71–81 (2022). https://doi.org/10.3103/S1066369X22090080

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  • DOI: https://doi.org/10.3103/S1066369X22090080

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