A Nonlocal Boundary Value Problem with the Frankl Condition for an Equation of Mixed Parabolic-Hyperbolic Type with the Fractional Gerasimov-Caputo Operator

被引：0

作者：

Islomov, B. I. ^{[1
]}

Akhmadov, I. A. ^{[1
]}

机构：

[1] Natl Univ Uzbekistan, Math Fac, Tashkent 100174, Uzbekistan

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2022年 / 43卷 / 03期

关键词：

nonlocal boundary conditions; parabolic-hyperbolic equation; fractional order equation; Wright's function; Green's function; Frankl problem; INTEGRODIFFERENTIAL EQUATION; DIFFERENTIAL-EQUATION; UNIQUE SOLVABILITY; INVERSE PROBLEM; TRICOMI;

D O I：

10.1134/S1995080222060129

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A new nonlocal boundary value problem with the Frankl condition for an equation of mixed parabolic-hyperbolic type with a fractional-order operator in the sense of Gerasimov-Caputo is formulated. The line of change of type is not a characteristic of the equation. The proposed new nonlocal condition connects the points on the boundaries of the parabolic part and the hyperbolic part of the domain. This problem is a generalization of well-known Frankl-type problems. The unique solvability of this problem is proved in the sense of the classical and strong solutions.

引用

页码：755 / 761

页数：7

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