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Uniqueness of the Solution of the Dirichlet Problem for a Multidimensional Differential Equation of Fractional Order

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Abstract

A partial differential equation of fractional order with an arbitrary number of independent variables is studied. For integer orders of fractional derivatives, the equation under consideration becomes a second-order linear elliptic equation with Laplace operator in the principal part. The Dirichlet problem in a multidimensional domain is considered. The extremum principle for the equation under study and the uniqueness of the solution of the problem under consideration in a bounded or an unbounded domain are proved.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Automation, 360000, Nalchik, Russia

    O. Kh. Masaeva

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  1. O. Kh. Masaeva
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Correspondence to O. Kh. Masaeva.

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Masaeva, O.K. Uniqueness of the Solution of the Dirichlet Problem for a Multidimensional Differential Equation of Fractional Order. Math Notes 109, 89–93 (2021). https://doi.org/10.1134/S0001434621010107

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  • DOI: https://doi.org/10.1134/S0001434621010107

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