## 1 Introduction
Initially, ordinary first-order constitutive equations were straightforwardly replaced with fractional counterparts [30; 31; 32; 33; 34]. An obvious drawback of this approach was its purely phenomenological character. An alternative approach implied physical representation of fractional constitutive equations via hierarchical combinations of dashpots and springs [35; 36; 37; 38]. This concept (so-called ladder models) has been successfully implemented in further studies by [PERSON] et al. [39] and [PERSON] et al. [40]. The authors have considered generalized viscoelastic models, replaced them with fractional ones, and obtained their analytical solutions in terms of relaxation modulus and creep compliance. Numerous studies have demonstrated the superiority of fractional calculus approach compared to classical one in predicting viscoelastic properties of materials and flows in various geometries. [PERSON] et al. [41] studied the behavior of relaxation modulus for polymethyl methacrylate (PMMA) and polytetrafluoroethelene (PTFE) and demonstrated much more accurate fitting of experimental data using fractional Maxwell model compared to integer-order one. [PERSON] et al. [42] proposed and experimentally verified the generalized fractional Maxwell model in the design of damper systems for seismic and vibration isolation. [PERSON] and coworkers [43] have studied the stress-relaxation behavior of fabrics coated with PTFE under various temperatures. The authors demonstrated the superiority of fractional Maxwell model in predicting stress-relaxation behavior. This behavior was experimentally proven to be nonlinear, while predicted to be linear by the classic Maxwell model. Moreover, compared to the generalized Maxwell model, the fractional one appeared to be much easier, as it did not require a large number of structural units to increase accuracy. The similar results for fractional Maxwell and fractional Zener models were obtained for elastomers (carbon-black filled resins) [44; 45; 46], polymers and rocks [47], and biological materials [48]. Fractional Kelvin-Voigt model was found to be efficient in predicting viscoelastic behavior of sludge [49]. Fractional calculus approach to viscoelasticity found applications not only for solids, as shown above, but also for various fluids. A brief historic retrospective reveals that both classic and fractional viscoelastic fluid flows in constrained geometries, especially pipes and ducts, turned out to be of a particular researchers' interest for about a century. This can be attributed to the fact that such geometries are widely used for practical applications and also admit relatively easy analytical solutions. Oscillatory pipe flows were among thoroughly investigated. Its classical consideration was traced back to 1920-1930s [50; 51]. These seminal studies were further extended and generalized by [PERSON], [PERSON], and others [52; 53; 54; 55]. Later researchers considered dynamics of oscillatory pipe flows at various Reynolds numbers [56; 57], both experimentally and theoretically, and specifically investigated transition to turbulence [58; 59]. The foundations of fractional derivatives towards fluids viscoelastic behavior were laid by [PERSON] and [PERSON] [29]. [PERSON] [60] studied viscoelastic transient flows in cylindrical pipes and annulus. [PERSON] et al. [61] provided a theoretical framework for oscillating viscoelastic pipe flow using fractional Maxwell model. The authors demonstrated a drastic difference in velocity profile compared to the integer-order Maxwell model. Viscoelastic start-up flow with the fractional Maxwell model was considered by [PERSON] et al. [62]. A similar problem in the annular pipe using fractional Burgers model was solved by [PERSON] et al. [63]. An unsteady viscoelastic flow in a cylinder [64] and rectangular duct [65] (using fractional Maxwell model) were also considered. The exact solutions of unsteady flow in cylindrical domains with Maxwell fractional model were derived by [PERSON] and [PERSON] [66; 67].