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
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 differ...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2022-12-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Online Access: | https://mathematics-vestnik.ksu.kz/apart/2022-108-4/9.pdf |
| Summary: | 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. |
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| ISSN: | 2518-7929 2663-5011 |