Dirichlet Problems for Mixed-Type Equations with Fractional Derivatives

被引：7

作者：

Sabitov, K. B. ^{[1
,2
]}

机构：

[1] Russian Acad Sci, Inst Math Comp Ctr, Subdiv Ufa Fed Res Ctr, Ufa 450008, Russia

[2] Bashkir State Univ, Sterlitamak Branch, Sterlitamak 453126, Russia

来源：

RUSSIAN MATHEMATICS | 2022年 / 66卷 / 09期

关键词：

mixed-type equation with fractional derivatives; Dirichlet problem; uniqueness criterion; existence; series; stability;

D O I：

10.3103/S1066369X22090080

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：71 / 81

页数：11

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