Stability analysis of multi-term fractional-differential equations with three fractional derivatives

TL;DR

This paper derives necessary and sufficient conditions for the stability and instability of multi-term linear fractional differential equations with three Caputo derivatives, providing fractional-order-dependent and independent characterizations.

Contribution

It offers new stability criteria for complex multi-term fractional differential equations with three derivatives, extending classical results to fractional-order systems.

Findings

Derived stability and instability conditions for multi-term fractional equations

Provided fractional-order-dependent and independent stability characterizations

Applied results to Basset, Bagley-Torvik, and fractional pendulum equations

Abstract

Necessary and sufficient stability and instability conditions are obtained for multi-term homogeneous linear fractional differential equations with three Caputo derivatives and constant coefficients. In both cases, fractional-order-dependent as well as fractional-order-independent characterisations of stability and instability properties are obtained, in terms of the coefficients of the multi-term fractional differential equation. The theoretical results are exemplified for the particular cases of the Basset and Bagley-Torvik equations, as well as for a multi-term fractional differential equation of an inextensible pendulum with fractional damping terms, and for a fractional harmonic oscillator.