New mathematical models in anomalous viscoelasticity from the derivative with respect to another function view point

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.