| Autor: |
Vladimir E. Fedorov, Nikolay V. Filin |
| Jazyk: |
angličtina |
| Rok vydání: |
2021 |
| Předmět: |
|
| Zdroj: |
Fractal and Fractional, Vol 5, Iss 1, p 20 (2021) |
| Druh dokumentu: |
article |
| ISSN: |
2504-3110 |
| DOI: |
10.3390/fractalfract5010020 |
| Popis: |
The aim of this work is to find by the methods of the Laplace transform the conditions for the existence of a strongly continuous resolving family of operators for a linear homogeneous equation in a Banach space with the distributed Gerasimov–Caputo fractional derivative and with a closed densely defined operator A in the right-hand side. It is proved that the existence of a resolving family of operators for such equation implies the belonging of the operator A to the class CW(K,a), which is defined here. It is also shown that from the continuity of a resolving family of operators at t=0 the boundedness of A follows. The existence of a resolving family is shown for A∈CW(K,a) and for the upper limit of the integration in the distributed derivative not greater than 2. As corollary, we obtain the existence of a unique solution for the Cauchy problem to the equation of such class. These results are used for the investigation of the initial boundary value problems unique solvability for a class of partial differential equations of the distributed order with respect to time. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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