This article is cited in 10 papers

The Dirichlet Problem for a mixed-type equation with fractional derivatives

K. B. Sabitov<sup>ab

a</sup> Institute of strategic researches of the Republic of Bashkortostan, 15 Kirova str., Ufa, 450077 Russia
^b Sterlitamak branch of Bashkir State University, 37 Lenina Ave., Sterlitamak, 453126 Russia

Abstract: In this paper we study the first boundary value problem for equation of mixed type with fractional derivatives in a rectangular domain. The criterion for the uniqueness of 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 this equations. The stability of the solution with respect to given boundary functions is established in the class of continuous and square-summable functions.

Keywords: the mixed-type equation with fractional derivatives, the Dirichlet problem, criterion of uniqueness, existence, series, stability.

UDC: 517.95

Received: 05.11.2021
Revised: 10.02.2022
Accepted: 08.04.2022

DOI: 10.26907/0021-3446-2022-9-83-94

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2022, 66:9, 71–81