New general fractional-order rheological models with kernels of Mittag-Leffler functions

摘要

In this paper, we consider new fractional-order Maxwell and Voigt models within the framework of the general fractional derivatives (GFDs). The operators are considered in the sense of Liouville-Caputo and Riemann-Liouville types GFDs involving the kernels of the Mittag-Leffler functions. The creep and relaxation characteristics for the fractional-order models are also discussed in detail. The formulations are proposed as useful tools to describe the complex behaviors of the general fractional-order viscoelasticity with memory effect.