EXACT STABILITY AND INSTABILITY REGIONS FOR TWO-DIMENSIONAL LINEAR AUTONOMOUS MULTI-ORDER SYSTEMS OF FRACTIONAL-ORDER DIFFERENTIAL EQUATIONS

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 characterised, in terms of the main diagonal elements of the systems' matrix, as well as its determinant.

Automated summary

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