Rheological analysis of the general fractional-order viscoelastic model involving the Miller-Ross kernel (Q2234601)

The paper introduces the general fractional-order derivative operator (GFODO) viscoelastic constitutive models within the Miller-Ross kernel in the sense of Liouville-Sonine type. This generalized fractional order shows its capability for exhibiting the stress history and creep compliance. To facilitate a better understanding of the development of the presented GFODO, the authors also present the essential concepts of the general fractional-order calculus. The authors present a comparison of the general fractional-order Kelvin-Voigt model with Miller-Ross kernel with the classical integer-order Kelvin-Voigt model and show that the general fractional model covers all stages of creep viz, primary creep, steady-state creep, and the tertiary creep stages whereas the classical integer models suffer from limitations in describing the tertiary stage creep. The authors enhance the value of the paper by including an extensive list of related references for further study for an interested reader.