This article is cited in 1 paper

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

O. Kh. Masaeva

Institute of Applied Mathematics and Automation, Nalchik

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.

Keywords: conditionally elliptic equations, Riemann–Liouville fractional derivative, Dirichlet problem.

UDC: 517.95

Received: 12.04.2019
Revised: 31.03.2020

DOI: 10.4213/mzm12415

 English version: Mathematical Notes, 2021, 109:1, 89–93

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