Boundary value problem for the heat equation with a load as the Riemann-Liouville fractional derivative

被引：5

作者：

Pskhu, A., V ^{[1
]}

Kosmakova, M. T. ^{[2
]}

Akhmanova, D. M. ^{[2
]}

Kassymova, L. Zh ^{[3
]}

Assetov, A. A. ^{[2
]}

机构：

[1] RAS, Kabardino Balkarian Sci Ctr, Inst Appl Math & Automat, Nalchik, Russia

[2] Karagandy Univ, Karaganda, Kazakhstan

[3] Karaganda Tech Univ, Karaganda, Kazakhstan

来源：

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS | 2022年 / 105卷 / 01期

关键词：

loaded equation; fractional derivative; Volterra integral equation; Wright function; unique solvability; CONDUCTION EQUATION; OPERATOR;

D O I：

10.31489/2022M1/74-82

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A boundary value problem for a fractionally loaded heat equation is considered in the first quadrant. The loaded term has the form of the Riemann-Liouville's fractional derivative with respect to the time variable, and the order of the derivative in the loaded term is less than the order of the differential part. The study is based on reducing the boundary value problem to a Volterra integral equation. The kernel of the obtained integral equation contains a special function, namely, the Wright function. The kernel is estimated, and the conditions for the unique solvability of the integral equation are obtained.

引用

页码：74 / 82

页数：9

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