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Colombaro, Ivano; Garra, Roberto; Giusti, Andrea; Mainardi, Francesco (2018): Scott-Blair models with time-varying viscosity. In: Applied Mathematics Letters, Vol. 86: pp. 57-63
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Abstract

In a recent paper, Zhou et al. (2017) studied the time-dependent properties of Glass Fiber Reinforced Polymers composites by employing a new rheological model with a time-dependent viscosity coefficient. This rheological model is essentially based on a generalized Scott-Blair body with a time-dependent viscosity coefficient. Motivated by this study, in this note we suggest a different generalization of the Scott-Blair model based on the application of Caputo-type fractional derivatives of a function with respect to another function. This new mathematical approach can be useful in viscoelasticity and diffusion processes in order to model systems with time-dependent features. In this paper we also provide the general solution of the creep experiment for our improved Scott-Blair model together with some explicit examples and illuminating plots.