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In this paper we investigate a general class of linear viscoelastic modelswhose creep and relaxation memory functions are expressed in Laplace domain bysuitable ratios of modified Bessel functions of contiguous order. In timedomain these functions are shown to be expressed by Dirichlet series (that isinfinite Prony series). It follows that the corresponding creep compliance andrelaxation modulus turn out to be characterized by infinite discrete spectra ofretardation and relaxation time respectively. As a matter of fact, we get aclass of viscoelastic models depending on a real parameter $\nu > -1$. Suchmodels exhibit rheological properties akin to those of a fractional Maxwellmodel (of order $1/2$) for short times and of a standard Maxwell model for longtimes.

A class of linear viscoelastic models based on Bessel functions