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

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.