Abstract
In this paper we propose the general Riemann-Liouville and Caputo-Liouville fractional derivatives with nonsingular power-law kernels, for the first time to our knowledge. New general laws of deformation within the framework of the general fractional derivatives are considered in detail. The creep and relaxation behaviors of the general fractional-order Voigt and Maxwell models are also obtained with the use of the Laplace transform. We provide the mathematical tools to describe the rheological phenomena of real materials with the memory effect.