论文标题
使用Prabhakar衍生物的分数订单系统的稳定性
Stability of fractional-order systems with Prabhakar derivatives
论文作者
论文摘要
Prabhakar类型的分数衍生物正在捕捉越来越多的兴趣，因为它们描述了异常的松弛现象（在介电和其他领域）表现出同时非本地性和非线性行为。在本文中，我们研究了具有Prabhakar衍生物的微分方程系统的渐近稳定性，从而提供了相应稳定区域的精确表征。 Prabhakar类型的线性微分方程和非线性系统的数值方法的渐近扩展（对于大小参数）得出了。因此，进行了数值实验以验证理论发现。
Fractional derivatives of Prabhakar type are capturing an increasing interest since their ability to describe anomalous relaxation phenomena (in dielectrics and other fields) showing a simultaneous nonlocal and nonlinear behaviour. In this paper we study the asymptotic stability of systems of differential equations with the Prabhakar derivative, providing an exact characterization of the corresponding stability region. Asymptotic expansions (for small and large arguments) of the solution of linear differential equations of Prabhakar type and a numerical method for nonlinear systems are derived. Numerical experiments are hence presented to validate theoretical findings.
