Fractional viscoelastic models with novel variable and constant order fractional derivative operators

Abstract

Abstract This paper deals with the application of a novel variable-order and constant-order fractional derivative without singular kernel of AtanganaKoca type to describe the fractional viscoelastic models, namely, fractional Maxwell model, fractional Kelvin-Voigt model, fractional Zener model and fractional Poynting-Thomson model. For each fractional viscoelastic model, the stress relaxation modulus and creep compliance are derived analytically under the variable-order and constant-order fractional derivative without singular kernel. Our results show that the relaxation modulus and creep compliance exhibit viscoelastic behaviors producing temporal fractality at different scales. For each viscoelastic model, the stress relaxation modulus and creep compliance are derived analytically under novel variable-order and constant-order fractional derivative with no singular kernel.