Abstract
In this article, we address the mathematical models in anomalous viscoelasticity containing the derivatives with respect to another function for the first time. The Newton-like, Maxwell-like, Kelvin-Voigt-like, Burgers-like, and Zener-like models via the new derivatives with respect to another functions are discussed in detail. The results for the calculus with respect to another function are as a new perspective proposed to present the better accuracy and efficiency in the descriptions of the complex behaviors of the materials.