具有Prabhakar导数的分数阶系统的稳定性
Stability of fractional-order systems with Prabhakar derivatives
摘要：
分数阶导数的Prabhakar型捕获越来越多的兴趣，因为他们的能力来描述异常松弛现象（在dielectric和其他领域），同时表现出非局部和非线性行为。本文研究了具有Prabhakar导数的微分方程系统的渐近稳定性，给出了相应的稳定区域的精确刻画。本文导出了Prabhakar型线性微分方程解的渐近展开式（对小变量和大变量）和非线性系统的数值方法。因此，数值实验验证理论研究结果。
英文摘要：
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.
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