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

Риман-Лиувилль бөлшек туындысы түрiндегi жүктемемен берiлген жылуөткiзгiштiк теңдеуi үшiн шекаралық есеп
Граничная задача для уравнения теплопроводности с нагрузкой в виде дробной производной Римана-Лиувилля
Pskhu A.V. Kosmakova M.T. Akhmanova D.M. Kassymova L.Zh. Assetov A.A.
2022 E.A. Buketov Karaganda University Publish house

Bulletin of the Karaganda University. Mathematics Series
2022 #105 Issue 1 74 - 82 pp.

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-Liouvilles 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.

fractional derivative , loaded equation , unique solvability , Volterra integral equation , Wright function

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Institute of Applied Mathematics and Automation, Kabardino-Balkarian Scientific Center of RAS, Nalchik, Russian Federation
Karagandy University of the name of academician E.A. Buketov, Karaganda, Kazakhstan
Karaganda Technical University, Karaganda, Kazakhstan

Institute of Applied Mathematics and Automation
Karagandy University of the name of academician E.A. Buketov
Karaganda Technical University

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