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## Archive of Issues

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. 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