Integral Representation for the Solutions of Autonomous Linear Neutral Fractional Systems with Distributed Delay

Ekaterina Madamlieva, Mihail Konstantinov, Marian Milev and Milena Petkova
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Ekaterina Madamlieva: Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria
Mihail Konstantinov: Department of Mathematics, University of Architecture, Civil Engineering and Geodesy, 1046 Sofia, Bulgaria
Marian Milev: Department of Matematics and Physics, University Of Food Technology, 4000 Plovdiv, Bulgaria
Milena Petkova: Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria

Mathematics, 2020, vol. 8, issue 3, 1-12

Abstract: The aim of this work is to obtain an integral representation formula for the solutions of initial value problems for autonomous linear fractional neutral systems with Caputo type derivatives and distributed delays. The results obtained improve and extend the corresponding results in the particular case of fractional systems with constant delays and will be a useful tool for studying different kinds of stability properties. The proposed results coincide with the corresponding ones for first order neutral linear differential systems with integer order derivatives.

Keywords: fractional derivatives; neutral fractional systems; distributed delay; integral representation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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