This article is cited in 1 paper

MATHEMATICS

Direct and inverse problems for the Hilfer fractional differential equation

R. R. Ashurov^ab, Yu. E. Fayziev^cd, N. M. Tukhtaeva<sup>a

a</sup> Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, ul. Universitetskaya, 9, Tashkent, 100174, Uzbekistan
^b Tashkent University of Applied Sciences, ul. Gavhar, 1, Tashkent, 100149, Uzbekistan
^c National University of Uzbekistan named after M. Ulugbek, Tashkent
^d University of Exact and Social Sciences, ul. Khalka Yoli, Kizgaldok, Tashkent district, Uzbekistan

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

Received: 07.03.2024
Accepted: 05.06.2024

DOI: 10.35634/vm240201

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