The phenomenological model for the heavy tracers in viscoelastic media modeled by a generalized Mittag-Leffler fractional Langevin equation with the generalized Stokes force, the Basset force, the Hookean force, and the thermal force has been revisited. Under the fluctuation-dissipation relation, the generalized Stokes force describes the viscoelastic media by a Mittag-Leffler (ML) memory kernel. Furthermore, based on the background of ML function, the generalized Mittag-Leffler fractional derivative is introduced. Moreover, the exact expression of stationary first moment and the expression of spectral amplification (SPA) of a tracer model have been deserved by the generalized form of Shapiro-Loginov formula. The generalized stochastic resonance (GSR) phenomena has been systematically studied. Moreover, the GSR, reverse stochastic resonance (SR) phenomenon, bona fide SR, stochastic multi-resonance (SMR) phenomena, increasing multi-resonance and decreasing multi-resonance have been found. Especially, the periodic resonance phenomenon could be induced by the generalized Mittag-Leffler (GML) noise, which has been few observed in the previous literatures.

中文翻译：

---

具有流体动力学相互作用的广义 Mittag-Leffler 分数 Langevin 方程的共振行为

重新审视了粘弹性介质中重示踪剂的唯象模型，该模型由具有广义 Stokes 力、Basset 力、Hookean 力和热力的广义 Mittag-Leffler 分数 Langevin 方程建模。在涨落-耗散关系下，广义斯托克斯力通过 Mittag-Leffler (ML) 记忆核来描述粘弹性介质。此外，基于ML函数的背景，介绍了广义的Mittag-Leffler分数导数。此外，Shapiro-Loginov 公式的广义形式应得于示踪模型的平稳一阶矩的精确表达和谱放大（SPA）的表达。广义随机共振（GSR）现象已得到系统研究。此外，GSR，已经发现了反向随机共振（SR）现象，真正的SR，随机多共振（SMR）现象，增加多共振和减少多共振。特别是，周期性共振现象可以由广义的米塔格-莱夫勒（GML）噪声引起，这在以前的文献中很少观察到。