A Perron-type theorem for fractional linear differential systems

TL;DR

This paper establishes a necessary and sufficient condition for the existence of bounded solutions in linear inhomogeneous fractional differential systems and characterizes all such solutions explicitly.

Contribution

It introduces a Perron-type theorem specifically for fractional linear differential systems, providing new theoretical insights and explicit solution descriptions.

Findings

Necessary and sufficient condition for bounded solutions

Explicit description of all bounded solutions

Theoretical framework for fractional differential systems

Abstract

We give a necessary and sufficient condition for a system of linear inhomogeneous fractional differential equations to have at least one bounded solution. We also obtain an explicit description for the set of all bounded (or decay) solutions for these systems.