Exact stability and instability regions for two-dimensional linear autonomous multi-order systems of fractional-order differential equations

TL;DR

This paper provides a complete characterization of stability and instability regions for two-dimensional linear autonomous fractional-order systems, based on matrix properties, enhancing understanding of fractional differential equations.

Contribution

It offers necessary and sufficient conditions for stability and instability in such systems, including fractional-order-dependent and independent criteria, which were not fully characterized before.

Findings

Derived explicit stability conditions based on matrix elements.

Characterized fractional-order-dependent and independent stability properties.

Established criteria applicable to a broad class of fractional-order systems.

Abstract

Necessary and sufficient conditions are explored for the asymptotic stability and instability of linear two-dimensional autonomous systems of fractional-order differential equations with Caputo derivatives. Fractional-order-dependent and fractional-order-independent stability and instability properties are fully characterized, in terms of the main diagonal elements of the systems' matrix, as well as its determinant.