On the Preservation with Respect to Nonlinear Perturbations of the Stability Property for Nonautonomous Linear Neutral Fractional Systems with Distributed Delays

Ekaterina Madamlieva, Hristo Kiskinov, Milena Petkova and Andrey Zahariev
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Ekaterina Madamlieva: Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria
Hristo Kiskinov: Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria
Milena Petkova: Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria
Andrey Zahariev: Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria

Mathematics, 2022, vol. 10, issue 15, 1-20

Abstract: In the present paper, sufficient conditions are obtained under which the Cauchy problem for a nonlinearly perturbed nonautonomous neutral fractional system with distributed delays and Caputo type derivatives has a unique solution in the case of initial functions with first-kind discontinuities. For this system, by applying a formula for the integral presentation of the solution of the nonhomogeneous linear neutral fractional system, we found some additional natural conditions to ensure that from the global asymptotically stability of the zero solution of the linear part of the nonlinearly perturbed system, global asymptotic stability of the zero solution of the whole nonlinearly perturbed system follows.

Keywords: fractional derivatives; neutral fractional systems; distributed delay; integral representation; asymptotic stability (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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