About the Resolvent Kernel of Neutral Linear Fractional System with Distributed Delays

Hristo Kiskinov (), Mariyan Milev and Andrey Zahariev
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Hristo Kiskinov: Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria
Mariyan Milev: Department of Mathematics, Physics and Information Technologies, University of Food Technology, 4002 Plovdiv, Bulgaria
Andrey Zahariev: Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria

Mathematics, 2022, vol. 10, issue 23, 1-17

Abstract: The present work considers the initial problem (IP) for a linear neutral system with derivatives in Caputo’s sense of incommensurate order, distributed delay and various kinds of initial functions. For the considered IP, the studied problem of existence and uniqueness of a resolvent kernel under some natural assumptions of boundedness type. In the case when, in the system, the term which describes the outer forces is a locally Lebesgue integrable function and the initial function is continuous, it is proved that the studied IP has a unique solution, which has an integral representation via the corresponding resolvent kernel. Applying the obtained results, we establish that, from the existence and uniqueness of a resolvent kernel, the existence and uniqueness of a fundamental matrix of the homogeneous system and vice versa follows. An explicit formula describing the relationship between the resolvent kernel and the fundamental matrix is proved as well.

Keywords: fractional derivatives; neutral fractional systems; distributed delay; integral representation; resolvent kernel (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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