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Russia Nalchik
Year
2019
Volume
29
Issue
4
Pages
459-482
>>
Section Mathematics
Title Nonlocal boundary value problems for a fractional-order convection-diffusion equation
Author(-s) Beshtokov M.Kh.a, Vodakhova V.A.b
Affiliations Institute of Applied Mathematics and Automation, Kabardino-Balkarian Scientific Center of the Russian Academy of Sciencesa, Kabardino-Balkarian State Universityb
Abstract In the rectangular region, we study nonlocal boundary value problems for the one-dimensional unsteady convection-diffusion equation of fractional order with variable coefficients, describing the diffusion transfer of a substance, as well as the transfer due to the motion of the medium. A priori estimates of solutions of nonlocal boundary value problems in differential form are derived by the method of energy inequalities. Difference schemes are constructed and analogs of a priori estimates in the difference form are proved for them, error estimates are given under the assumption of sufficient smoothness of solutions of equations. From the obtained a priori estimates, the uniqueness and stability of the solution from the initial data and the right part, as well as the convergence of the solution of the difference problem to the solution of the corresponding differential problem at the rate of $O(h^2+\tau^2)$.
Keywords nonlocal boundary value problems, a priori estimate, nonstationary convection-diffusion equation, fractional order differential equation, fractional Caputo derivative
UDC 519.63
MSC 35K10
DOI 10.20537/vm190401
Received 31 March 2019
Language Russian
Citation Beshtokov M.Kh., Vodakhova V.A. Nonlocal boundary value problems for a fractional-order convection-diffusion equation, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2019, vol. 29, issue 4, pp. 459-482.
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