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Rheological complex models of various elastoviscous and viscoelastic fractional-type substances with polarized piezoelectric properties are of interest due to the widespread use of viscoelastic–plastic bodies under loading. The word “overview” used in the title means and corresponds to the content of the manuscript and aims to emphasize that it presents an overview of a new class of complex rheological models of the fractional type of ideal elastoviscous, as well as viscoelastic, materials with piezoelectric properties. Two new elementary rheological elements were introduced: a rheological basic Newton’s element of ideal fluid fractional type and a basic Faraday element of ideal elastic material with the property of polarization under mechanical loading and piezoelectric properties. By incorporating these newly introduced rheological elements into classical complex rheological models, a new class of complex rheological models of materials with piezoelectric properties described by differential fractional-order constitutive relations was obtained. A set of seven new complex rheological models of materials are presented with appropriate structural formulas. Differential constitutive relations of the fractional order, which contain differential operators of the fractional order, are composed. The seven new complex models describe the properties of ideal new materials, which can be elastoviscous solids or viscoelastic fluids. The purpose of the work is to make a theoretical contribution by introducing, designing, and presenting a new class of rheological complex models with appropriate differential constitutive relations of the fractional order. These theoretical results can be the basis for further scientific and applied research. It is especially important to point out the possibility that these models containing a Faraday element can be used to collect electrical energy for various purposes. Full article

Two rheological Burgers–Faraday models and rheological dynamical systems were created by using two new rheological models: Kelvin–Voigt–Faraday fractional-type model and Maxwell–Faraday fractional-type model. The Burgers–Faraday models described in the paper are new models that examine the dynamical behavior of materials with coupled fields: mechanical stress and strain and the electric field of polarization through the Faraday element. The analysis of the constitutive relation of the fractional order for Burgers–Faraday models is given. Two Burgers–Faraday fractional-type dynamical systems were created under certain approximations. Both rheological Burgers-Faraday dynamic systems have two internal degrees of freedom, which are introduced into the system by each standard light Burgers-Faraday bonding element. It is shown that the sequence of bonding elements in the structure of the standard light Burgers-Faraday bonding element changes the dynamic properties of the rheological dynamic system, so that in one case the system behaves as a fractional-type oscillator, while in the other case, it exhibits a creeping or pulsating behavior under the influence of an external periodic force. These models of rheological dynamic systems can be used to model new natural and synthetic biomaterials that possess both viscoelastic/viscoplastic and piezoelectric properties and have dynamical properties of stress relaxation. Full article