To solving the fractionally loaded heat equation

被引：8

作者：

Kosmakova, M. T. ^{[1
]}

Iskakov, S. A. ^{[1
]}

Kasymova, L. Zh ^{[1
,2
]}

机构：

[1] Buketov Karaganda Univ, Karaganda, Kazakhstan

[2] Karaganda State Tech Univ, Karaganda, Kazakhstan

来源：

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS | 2021年 / 101卷 / 01期

关键词：

loaded equation; fractional derivative; heat equation; Volterra integral equation; special function;

D O I：

10.31489/2021M1/65-77

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we consider a boundary value problem for a fractionally loaded heat equation in the class of continuous functions. Research methods are based on an approach to the study of boundary value problems, based on their reduction to integral equations. The problem is reduced to a Volterra integral equation of the second kind by inverting the differential part. We also carried out a study the limit cases for the fractional derivative order of the term with a load in the heat equation of the boundary value problem. It is shown that the existence and uniqueness of solutions to the integral equation depends on the order of the fractional derivative in the loaded term.

引用

页码：65 / 77

页数：13

共 21 条

[1] Boundary value problems for a spectrally loaded heat operator with load line approaching the time axis at zero or infinity [J].