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

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