论文标题
具有三个分数衍生物的多项分数方程的稳定性分析
Stability analysis of multi-term fractional-differential equations with three fractional derivatives
论文作者
论文摘要
对于具有三个Caputo衍生物和恒定系数的多项均匀线性分数方程，获得了必要和足够的稳定性和不稳定性条件。在这两种情况下，就多项分数微分方程的系数而言，获得了稳定性和不稳定性特性的分数依赖性和分数独立于稳定性和不稳定性的特征。在贝塞和巴格利 - 托尔维克方程的特定情况下，以及具有分数阻尼项的不可延迟的摆和分数和谐振荡器的多项分数微分方程的特定情况，以及分数谐波振动器的多项分数微分方程。
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.
