## 1 Introduction  
The engineering design process is a collective task that includes finding innovative ways to create products that are functional and meet clients' wants and needs, as well as planning, testing and improving the design. In order to predict, analyze and control the complex behavior of engineering systems and accelerate the design process, modeling and engineering simulations have been intensively used in the last few decades. The potential of artificial neural networks (ANNs) as a modeling technique in modern product development has been conclusively proven [1; 2; 3; 4]. In particular, ANNs are applicable also in product form design problems. This bio-inspired intelligence approach has been applied recently in planning, decision-making, forecasting, optimization, automation and other activities related to product form design analysis. For example, the paper [5] addressed a neural network-based approach for product design. The authors in [6] considered fuzzy neural networks as an integral part of a hybrid technique used in an automatic product form search. The proposed neural network approach has been also applied in optimization tasks in accordance with the designer's required product form. The paper [7] used neural network models to analyze the best design combination of product form elements. The authors in [8] proposed an ANN model to relate design parameters and produce a product form aesthetics design depending on customer perceptions in a more systematic and intelligent manner. The paper [9] considered a hybrid product form design method based on a specific class of ANNs from the perspective of multi-objective optimization. The paper [10] considers a number of ANN models, examining how a given product form affects the product image as perceived by customers. In [11], an ANN-based method is proposed to quantify the design preferences regarding product forms. In fact, product form design is an integrative part of the industrial design process since \"industrial design balanced the tensions between form and function, machine and human experience\" [12]. The shift from decorative arts to modernism was captured in the late 1800s by architect [PERSON], who stated that \"form follows function\" [13]. The above key principle of modernism influenced a new design language that emphasized geometry, precision, simplicity and economy in product form design. The influential Bauhaus school, which grew out of modernism, developed design principles that can be applied to any product [14]. Later, form formation and form classification in industrial design and architecture were systematically explored in [15; 16]. Recently, industrial designers have sought to incorporate advances in technology and artificial intelligence into product form design to create aerodynamic curves, groove lines and wing tails that exemplify speed and technological progress [12]. The ANN approach used does not only help to improve existing functionalities, but also changes the ways that products can be designed. Despite the advantages of employing ANN models in product form design problems, the number of existing results in the area is still not satisfactory. This is due mainly to the fact that applying neural network models in product form design analysis is a very complicated process that includes the construction of the neural network model; the exploration of the inputs, outputs and connection coefficients; training, etc. Furthermore, the current state of this research area mainly shows the usage of integer-order ANN models. However, fractional calculus offers a more flexible mechanism that has not been completely applied to the ANN models in the product form design area. Fractional-order models are relevant and significant in numerous scientific areas of study. The generalization, flexibility and nonlocality offered by fractional-order methods make them important and useful in solving various types of fractional-order problems in science, engineering and technology [17; 18; 19].