Creep and relaxation tests, performed on various materials like polymers, rubbers
and so on are well-tted by power-laws with exponent 2 [0; 1] (Nutting (1921), Di Paola et
al. (2011)). The consequence of this observation is that the stress-strain relation of hereditary
materials is ruled by fractional operators (Scott Blair (1947), Slonimsky (1961)). A large amount
of researches have been performed in the second part of the last century with the aim to connect
constitutive fractional relations with some mechanical models by means of fractance trees and
ladders (see Podlubny (1999)). Recently, Di Paola and Zingales (2012) proposed a mechanical
model that corresponds to fractional stress-strain relation with any real exponent and they have
proposed a description of above model (Di Paola et al. (2012)). In this study the authors aim
to extend the study to cases with more fractional phases and to fractional Kelvin-Voigt model
of hereditariness
