Article

Direct and inverse problems for the Hilfer fractional differential equation

Ravshan AshurovYu.E. FayzievNational University of Uzbekistan; University of Exact and Social SciencesNazokat TukhtaevaInstitute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan

Vestnik Udmurtskogo Universiteta Matematika Mekhanika Komp yuternye Naukijournal2024en

ABI

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.

Topics

Differential Equations and Boundary Problems Differential Equations and Numerical Methods Nonlinear Differential Equations Analysis

Identifiers

DOI: 10.35634/vm240201

Citations and references

Cited by 1 23 references

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