DOAJ Open Access 2022

On the non-uniqueness of the solution to a boundary value problem of heat conduction with a load in the form of a fractional derivative

M.T. Kosmakova K.A. Izhanova A.N. Khamzeyeva

Abstrak

The paper deals with the second boundary value problem for the loaded heat equation in the first quadrant. The loaded term contains a fractional derivative in the Caputo sense of an order α, 2 < α < 3. The boundary value problem is reduced to an integro-differential equation with a difference kernel by inverting the differential part. It is proved that a homogeneous integro-differential equation has at least one non-zero solution. It is shown that the solution of the homogeneous boundary value problem corresponding to the original boundary value problem is not unique, and the load acts as a strong perturbation of the boundary value problem.

Topik & Kata Kunci

Analysis Analytic mechanics Probabilities. Mathematical statistics

Penulis (3)

M.T. Kosmakova

K.A. Izhanova

A.N. Khamzeyeva

Format Sitasi

APA MLA BibTeX

Kosmakova, M., Izhanova, K., Khamzeyeva, A. (2022). On the non-uniqueness of the solution to a boundary value problem of heat conduction with a load in the form of a fractional derivative. https://doi.org/10.31489/2022m4/98-106

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Informasi Jurnal

Tahun Terbit: 2022
Sumber Database: DOAJ
DOI: 10.31489/2022m4/98-106
Akses: Open Access ✓