To solving the fractionally loaded heat equation
Жойылатын облыстағы жылуөткiзгiштiктiң екiөлшемдi шекаралық есебiнiң шешуiне
К решению двумерной граничной задачи теплопроводности в вырождающейся области
Kosmakova M.T. Iskakov S.A. Kasymova L.Zh.
2021E.A.Buketov Karaganda State University Publish House
Bulletin of the Karaganda University. Mathematics Series
2021#101Issue 165 - 77 pp.
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.
fractional derivative , heat equation , loaded equation , special function , Volterra integral equation
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Buketov Karaganda University, Karaganda, Kazakhstan
Karaganda Technical University, Karaganda, Kazakhstan
Buketov Karaganda University
Karaganda Technical University
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