## 1 Introduction  
The very first consideration of the problem involving fractional differential equation is traced back to the very end of the seventeenth century. It was [PERSON] who introduced the notation \(d^{n}/dx^{n}\) and [PERSON] who asked [PERSON]: \"What if \(n\) be \(1/2\)?\". [PERSON] response to this question has laid the foundations of what is today known as fractional calculus (FC) [1]. Despite these early attempts made by outstanding minds who were definitely ahead of their time, further development towards practical applications appeared to be somewhat slow. An interested reader can refer to an excellent review of [PERSON] for details on early stages of FC development [2]. The fundamentals of FC along with a brief applications overview can be found in classical books by [PERSON] and [PERSON] [3], [PERSON] [4], or more recent one by [PERSON] [5]. In the following decades it became obvious that with the incredible potential of FC to tackle problems in absolutely different fields, each of them should be addressed separately. By these means the general approaches in solving fractional differential equations could be tailored to reflect the specifics of a given field, optimize solution process, and formulate reliable constraints and ranges for, sometimes, purely mathematical parameters. Along these lines, readers with a background in physics can refer to [6; 7; 8; 9], while those from the engineering field can refer to [10; 11]. The comprehensive overview summarizing state-of-the-art practical applications of FC has been recently published by The Royal Society Publishing. The sixteen-paper issue entitled \"Advanced materials modeling via fractional calculus: challenges and perspectives\" [12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27] covers applications of constant-order (CO) and variable-order (VO) fractional differential operators to several fundamental phenomena. These include anomalous diffusion, [13; 16] heat conduction [14; 27], fractional viscoelasticity of fluids [19], and materials [12; 18; 22]. The approach to model viscoelastic properties of materials with VO FC operators is undoubtedly among the most promising ones, as it allows for the consideration of fractional order dynamics with respect to time, space, and material variables [22]. Viscoelasticity has been in the scope of researchers' interest since the nineteenth century and has gone through gradual development. With mathematical apparatus available at the time, several mechanical models have been proposed, developed, and generalized to address the problem of a more accurate description of material properties observed. Those classical models named after researchers who made a significant contribution to the field include but are not limited to [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON]. Based on two principal elements, spring and dashpot, connected in series and/or in parallel, those models met the needs of adequate material response description towards stresses and strains applied. However, as it often happened, experimental results started to accumulate, which illustrated the behaviors beyond the above-mentioned models. This issue was addressed from scratch, namely via rethinking of a basic element by [PERSON] in 1947 [28]. He came up with an idea of considering a single element capable of a simultaneous description of viscous and elastic properties of the material. This approach capitalized on a notion of fractional derivative and allowed for the alteration of the balance between viscous and elastic properties without any additional complexity, but covering a wide range of materials. The systematic study of fractional calculus applications to viscoelasticity was made by [PERSON] and [PERSON] [29], who laid theoretical foundations of this approach. Since that time the field had emerged, especially when biomedical applications were outlined. Historically, several approaches were developed to implement balancing between viscous and elastic properties of materials.