Open AccessBoundary value problem for the heat equation with a load as the Riemann-Liouville fractional derivative
Author(s) -
A.V. Pskhu,
M.T. Kosmakova,
D.M. Akhmanova,
L.Zh. Kassymova,
A.A. Assetov
Publication year - 2022
Publication title -
ķaraġandy universitetìnìn̦ habaršysy. matematika seriâsy
Language(s) - English
Resource type - Journals
eISSN - 2663-5011
pISSN - 2518-7929
DOI - 10.31489/2022m1/74-82
Subject(s) - mathematics , mathematical analysis , boundary value problem , heat kernel , fractional calculus , integral equation , partial differential equation , summation equation , heat equation , derivative (finance) , volterra integral equation , integro differential equation , differential equation , first order partial differential equation , financial economics , economics
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.