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.

Prabhakar类型的分数导数引起了越来越多的兴趣，因为它们描述异常弛豫现象（在电介质和其他领域）的能力显示了同时的非局部和非线性行为。在本文中，我们研究了带有Prabhakar导数的微分方程系统的渐近稳定性，提供了相应稳定性区域的精确表征。推导了Prabhakar型线性微分方程解的渐近展开式（适用于大参数和大参数）以及非线性系统的数值方法。因此，提出了数值实验以验证理论发现。