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


Kosmakova M.T. Izhanova K.A. Khamzeyeva A.N.
2022E.A.Buketov Karaganda State University Publish House

Bulletin of the Karaganda University. Mathematics Series
2022#108Issue 498 - 106 pp.

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.

Caputo fractional derivative , loaded equation , non-unique solvability , second boundary value problem , strong perturbation

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Karagandy University of the name of academician E.A. Buketov, Karaganda, Kazakhstan

Karagandy University of the name of academician E.A. Buketov

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