2021
DOI: 10.29229/uzmj.2021-3-2
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Initial-boundary value problem for a time-fractional subdiffusion equation on the torus

Abstract: An initial-boundary value problem for a time-fractional subdiffusion equation with the Riemann-Liouville derivatives on N-dimensional torus is considered. Uniqueness and existence of the classical solution of the posed problem are proved by the classical Fourier method. Sufficient conditions for the initial function and for the right-hand side of the equation are indicated, under which the corresponding Fourier series converge absolutely and uniformly. It should be noted, that the condition on the initial functio… Show more

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Cited by 2 publications
(8 citation statements)
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“…A result similar to Theorem 2 was obtained in the recent paper [8] for a subdiffusion equation with the Riemann-Liouville derivative. But the condition found for the initial function ϕ(x) in that work is less restrictive.…”
Section: Resultssupporting
confidence: 78%
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“…A result similar to Theorem 2 was obtained in the recent paper [8] for a subdiffusion equation with the Riemann-Liouville derivative. But the condition found for the initial function ϕ(x) in that work is less restrictive.…”
Section: Resultssupporting
confidence: 78%
“…The authors of papers [7], [8] and [9] used the Fourier method to construct a classical solution of the subdiffusion equations with the Riemann-Liouville derivative and various elliptic operators.…”
Section: Resultsmentioning
confidence: 99%
“…A result similar to Theorem 1.2 was obtained in the recent paper [8] for a subdiffusion equation with the Riemann-Liouville derivative. But the condition found for the initial function ϕ(x) in that work is less restrictive.…”
Section: Resultssupporting
confidence: 75%
“…In conclusion, note that a similar result with Theorem 1.2 for equation (1.1) with the Riemann-Liouville derivative is valid for all functions ϕ ∈ C(T N ) ∩ L a−2 2 (T N ) (see [8]).…”
Section: Counterexamplesupporting
confidence: 63%
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