Geodesic
Direct and inverse problems for the Hilfer fractional differential equation
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 2, pp. 167-181

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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, inverse problems
Mots-clés : subdiffusion equation 
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     title = {Direct and inverse problems for the {Hilfer} fractional differential equation},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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R. R. Ashurov; Yu. E. Fayziev; N. M. Tukhtaeva. Direct and inverse problems for the Hilfer fractional differential equation. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 2, pp. 167-181. http://geodesic.mathdoc.fr/item/VUU_2024_34_2_a0/