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Open AccessArticle

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

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Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria
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Department of Mathematics, University of Architecture, Civil Engineering and Geodesy, 1046 Sofia, Bulgaria
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Department of Matematics and Physics, University Of Food Technology, 4000 Plovdiv, Bulgaria
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 364; https://doi.org/10.3390/math8030364
Received: 1 February 2020 / Revised: 2 March 2020 / Accepted: 2 March 2020 / Published: 6 March 2020
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. View Full-Text
Keywords: fractional derivatives; neutral fractional systems; distributed delay; integral representation fractional derivatives; neutral fractional systems; distributed delay; integral representation
MDPI and ACS Style

Madamlieva, E.; Konstantinov, M.; Milev, M.; Petkova, M. Integral Representation for the Solutions of Autonomous Linear Neutral Fractional Systems with Distributed Delay. Mathematics 2020, 8, 364.

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