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Uzbekistan Kizgaldok, Tashkent district; Tashkent
Year
2024
Volume
34
Issue
2
Pages
167-181
>>
Section Mathematics
Title Direct and inverse problems for the Hilfer fractional differential equation
Author(-s) Ashurov R.R.ab, Fayziev Yu.E.cd, Tukhtaeva N.M.a
Affiliations Institute of Mathematics, National Academy of Sciences of Uzbekistana, Tashkent University of Applied Sciencesb, National University of Uzbekistanc, University of Exact and Social Sciencesd
Abstract The article studies direct and inverse problems for subdiffusion equations involving a Hilfer fractional derivative. An arbitrary positive self-adjoint operator $A$ is taken as the elliptic part of the equation. In particular, as the operator $A$ we can take the Laplace operator with the Dirichlet condition. First, the existence and uniqueness of a solution to the direct problem is proven. Then, using the representation of the solution to the direct problem, the existence and uniqueness of the inverse problem of finding the right-hand side of the equation, which depends only on the spatial variable, is proved.
Keywords Cauchy problems, Hilfer derivatives, subdiffusion equation, inverse problems
UDC 517.95
MSC 35R11, 34A12
DOI 10.35634/vm240201
Received 7 March 2024
Language Russian
Citation Ashurov R.R., Fayziev Yu.E., Tukhtaeva N.M. Direct and inverse problems for the Hilfer fractional differential equation, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2024, vol. 34, issue 2, pp. 167-181.
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