Integral Representation of the Solutions for Neutral Linear Fractional System with Distributed Delays
FRACTAL AND FRACTIONAL(2021)
Abstract
In the present paper, first we obtain sufficient conditions for the existence and uniqueness of the solution of the Cauchy problem for an inhomogeneous neutral linear fractional differential system with distributed delays (even in the neutral part) and Caputo type derivatives, in the case of initial functions with first kind discontinuities. This result allows to prove that the corresponding homogeneous system possesses a fundamental matrix C(t,s) continuous in t,t & ISIN;[a,& INFIN;),a & ISIN;R. As an application, integral representations of the solutions of the Cauchy problem for the considered inhomogeneous systems are obtained.
MoreTranslated text
Key words
fractional derivatives,neutral fractional systems,distributed delay,integral representation
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined