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

A.V. Pskhu | Zendy; M.T. Kosmakova | Zendy; D.M. Akhmanova | Zendy; L.Zh. Kassymova | Zendy; A.A. Assetov | Zendy

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Boundary 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 -

bulletin of the karaganda university-mathematics

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 , fractional calculus , heat kernel , derivative (finance) , partial differential equation , summation equation , integral equation , heat 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.

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