Article
Version 1
Preserved in Portico This version is not peer-reviewed
On the Nonlocal Problems in Time for Time-fractional Subdiffusion Equations
*
and
Version 1
: Received: 22 November 2021 / Approved: 24 November 2021 / Online: 24 November 2021 (12:44:07 CET)
A peer-reviewed article of this Preprint also exists.
Ashurov, R.; Fayziev, Y. On the Nonlocal Problems in Time for Time-Fractional Subdiffusion Equations. Fractal Fract. 2022, 6, 41. Ashurov, R.; Fayziev, Y. On the Nonlocal Problems in Time for Time-Fractional Subdiffusion Equations. Fractal Fract. 2022, 6, 41.
Abstract
The nonlocal boundary value problem, dtρu(t)+Au(t)=f(t) (0<ρ<1, 0<t≤T), u(ξ)=αu(0)+φ (α is a constant and 0<ξ≤T), in an arbitrary separable Hilbert space H with the strongly positive selfadjoint operator A, is considered. The operator dt on the left hand side of the equation expresses either the Caputo derivative or the Riemann-Liouville derivative; naturally, in the case of the Riemann - Liouville derivatives, the nonlocal boundary condition should be slightly changed. Existence and uniqueness theorems for solutions of the problems under consideration are proved. The influence of the constant α on the existence of a solution to problems is investigated. Inequalities of coercivity type are obtained and it is shown that these inequalities differ depending on the considered type of fractional derivatives. The inverse problems of determining the right-hand side of the equation and the function φ in the boundary conditions are investigated.
Keywords
Nonlocal problems; the Riemann-Liouville and the Caputo derivatives; subdiffusion equation; inverse problems
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
