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Cauchy Problem for an Abstract Evolution Equation of Fractional Order

Fractal and Fractional. 2023. Vol. 7. No. 2. Article 111.
Maksim V. Kukushkin

In this paper, we define an operator function as a series of operators corresponding to the
Taylor series representing the function of the complex variable. In previous papers, we considered
the case when a function has a decomposition in the Laurent series with the infinite principal part
and finite regular part. Our central challenge is to improve this result having considered as a regular
part an entire function satisfying the special condition of the growth regularity. As an application, we
consider an opportunity to broaden the conditions imposed upon the second term not containing the
time variable of the evolution equation in the abstract Hilbert space.

Research target: Mathematics
Language: English
Full text
DOI
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Keywords: Operator theoryEvolution equations
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