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The purpose of this paper is to develop a novel multivariate fractional grey model termed GM(a, n) based on the classical GM(1, n) model. The new model can provide accurate prediction with more freedom, and enrich the content of grey theory.

The GM(α, n) model is systematically studied by using the grey modelling technique and the forward difference method. The optimal fractional order a is computed by the genetic algorithm. Meanwhile, a stochastic testing scheme is presented to verify the accuracy of the new GM(a, n) model.

The recursive expressions of the time response function and the restored values of the presented model are deduced. The GM(1, n), GM(a, 1) and GM(1, 1) models are special cases of the model. Computational results illustrate that the GM(a, n) model provides accurate prediction.

The GM(a, n) model is used to predict China’s total energy consumption with the raw data from 2006 to 2016. The superiority of the GM(a, n) model is more freedom and better modelling by fractional derivative, which implies its high potential to be used in energy field.

It is the first time to investigate the multivariate fractional grey GM(α, n) model, apply it to study the effects of China’s economic growth and urbanization on energy consumption.

Sand production is a challenging issue during hydrocarbon production in the oil and gas industry. This paper aims to investigate one sand production process, i.e. transient sand production, using a novel bonded particle lattice Boltzmann method. This mesoscopic technique provides a unique insight into complicated sand erosion process during oil exploitation.

The mesoscopic fluid-particle coupling is directly approached by the immersed moving boundary method in the framework of lattice Boltzmann method. Bonded particle method is used for resolving the deformation of solid. The onset of grain erosion of rocks, which are modelled by a bonded particle model, is realised by breaking the bonds simulating cementation when the tension or tangential force exceeds critical values.

It is proved that the complex fluid–solid interaction occurring at the pore/grain level can be well captured by the immersed moving boundary scheme in the framework of the lattice Boltzmann method. It is found that when the drawdown happens at the wellbore cavity, the tensile failure area appears at the edge of the cavity. Then, the tensile failure area gradually propagates inward, and the solid particles at the tensile failure area become fluidised because of large drag forces. Subsequently, some eroded particles are washed out. This numerical investigation is demonstrated through comparison with the experimental results. In addition, through breaking the cementation, which is simulated by bond models, between bonded particles, the transient particle erosion process is successfully captured.

A novel bonded particle lattice Boltzmann method is used to investigate the sand production problem at the grain level. It is proved that the complex fluid–solid interaction occurring at the pore/grain level can be well captured by the immersed moving boundary scheme in the framework of the lattice Boltzmann method. Through breaking the cementation, which is simulated by bond models, between bonded particles, the transient particle erosion process is successfully captured.

The use of removable complete dentures is a selectable restorative procedure for edentulous patients. To improve the fabrication quality and efficiency of removable complete dentures, this paper aims to introduce a new method to fabricate customized wax complete dentures with additive manufacturing. This process uses complementary digital technologies, and allows faster and better manufacture of complete dentures.

In the study, a dental scanner was used to obtain surface data from edentulous casts and rims made by the dentist. A parameterized three-dimensional graphic database of artificial teeth was pre-established. Specialized computer-aided design software was used to set up the artificial dentition and design the esthetic gingiva and base plate. A selective laser sintering machine was used to transfer the data from stereolithography files into a wax base plate with location holes for each artificial tooth.

Under this method, a set of wax base plates with 28 location holes available for the placement of the artificial teeth were designed and fabricated within 6 h. The try-in wax dentures fitted the patient’s mouth well, besides occlusion relationships. Then, the occlusion relationships can be adjusted manually to achieve a balanced centric occlusion.

This method can be used to design and fabricate wax try-in removable complete dentures semi-automatically and rapidly; however, the algorithm for the occlusion contact design needs to be improved.

The purpose of this paper is to study a fractional grey model FAGM(1,1,t^α) based on the GM(1,1,t^α) model and the fractional accumulated generating operation, and then predict the national health expenditure, the government health expenditure and the out-of-pocket health expenditure of China.

The presented univariate grey model is systematically studied by using the grey modelling technique, the fractional accumulated generating operation and the trapezoid approximation formula of definite integral. The optimal system parameters r and α are evaluated by the particle swarm optimisation algorithm.

The expressions of the time response function and the restored values of this model are derived. The GM(1,1), NGM(1,1,k,c) and GM(1,1,t^α) models are particular cases of the FAGM(1,1,t^α) model with deterministic r and α. Compared with other forecasting models, the results of the FAGM(1,1,t^α) model have higher precision.

The superiority of the new model has high potential to be used in the medicine and health fields and others. Results can provide a guideline for government decision making.

The univariate fractional grey model FAGM (1,1,t^α) successfully studies the China’s health expenditure.

In this paper, the authors study the effect of consumers' fairness preferences on dynamic pricing strategies adopted by platforms in a non-cooperative game.

This study applies fair game and repeated game theory.

This study reveals that, in a one-shot game, if consumers have fairness preferences, dynamic prices will slightly decline. In a repeated game, dynamic prices will be reduced even when consumers do not have fairness preferences. When fairness preferences and repeated game are considered simultaneously, dynamic prices are most likely to be set at fair prices. The authors also discuss the effect of platforms' discounting factors, the consumers' income and alternative choices of consumption on the dynamic prices.

The study findings illustrate the importance of incorporating behavioral elements in understanding and designing the dynamic pricing strategies for platforms and the implications on social welfare in general.

The authors developed a theoretical model to incorporate consumers' fairness preference into the decision-making process of platforms when they design the dynamic pricing strategies.

Based on theories related to coopetition, the purpose of this paper is to examine the patterns of business-to-business digital referrals inscribed in businesses’ digital content.

A complete industry-wise digital data set is formed by extracting digital referrals in all the content pages. The authors outline how digital referrals are strategically used among peer businesses in the peer-to-peer digital network and in the augmented digital network, taking into consideration geographical framing and physical distance.

The authors reveal how geographical framing and physical distance influence peer-to-peer referral patterns in the digital space. Quite counter-intuitively, businesses are more likely to give digital referrals for peers residing in the same region, as well as for peers located in closer proximity. Further, results from the augmented digital network show that peer businesses in closer proximity exhibit greater strategic similarity in their digital referring strategy.

The findings extend the understanding of business-to-business coopetition to the digital space and suggest that geographical framing and physical distance can induce reciprocated relationships between peers by offering each other digital referrals.

The findings shed light on the formation of a business-to-business digital coopetition strategy using digital referral marketing.

This study highlights the impact of digital referrals in business-to-business relationship management, especially in the digital coopetition context.

From an institutional theory perspective, the purpose of this paper is to investigate the combined impact of financial capital (microcredit) and human capital development (entrepreneurship training) delivered by financial non-governmental organisations (FNGOs) on the performance of micro and small enterprises (MSEs) in Ghana.

Adopting a multiple linear regression analysis, the study used primary data collected from 506 Ghanaian MSEs. Microcredit was measured using four main constructs, namely, loan cost, loan amount, the flexibility of loan repayment and loan accessibility. Entrepreneurship training was measured using four main constructs, namely, training content, training efficiency, training frequency and training accessibility. MSE performance was also measured using three main indicators, namely, sales, employment and profitability growth. The study controlled for business age, industry category, manager’s educational level and gender.

The results of this study show that the combined delivery of financial and human capital development by FNGOs has a significant impact on MSE performance. The social welfare logic adopted by FNGOs seems to be legitimate to the needs and growth of MSEs in Ghana. However, the cost of microcredit remains a drawback, constraining the performance of MSEs in Ghana.

This study was carried out in the Volta Region, which is one of the ten regions of Ghana. Even though the sample size suffices, the findings from this study could not be generalised to the whole of Ghana. Also, this study is a quantitative study and could benefit from a triangulated method where the qualitative inputs could offer insights into the findings in this study.

Theoretically, this study contributes to the understanding of institutions and the type of impact they have on the growth of MSEs. Practically, the provision of a conducive environment and access to financial capital is crucial to the growth of MSEs. Also, the adoption of the social welfare logic in microfinance delivery could be one of the major steps in promoting the performance of MSEs in Ghana.

Dynamic capabilities are regarded as the bedrock of businesses that survive in a dynamic environment. Building upon the social capital theory, the purpose of this paper is to investigate the nexus between dynamic capabilities and social capital in family businesses.

The study adopted a quantitative approach. As there is no formal business database available in China, the study followed a snowball sampling procedure. In total, 628 useful responses were gathered.

The study echoes the call of Arregle et al. (2007) for understanding family business’s internal sources of competitiveness and the role of social capital. Results show that the three dimensions of social capital, namely, structural, cognitive, and relational capital, influence dynamic capabilities of family businesses.

The lack of an official business database in China made the conventional representative sample survey used in the West difficult to replicate. Furthermore, empirical data were collected from different regions of China; regional cultures and different levels of economic development across the regions might influence the social capital-dynamic capabilities connection, but these were not examined in the current study.

The study integrates two significant but disconnected research streams, i.e. social capital and dynamic capabilities. Furthermore, the study shows how different dimensions of social capital influence dynamic capabilities. Research findings derived may contribute to the entrepreneurial debate as to why some family businesses can survive in the dynamic environment while others cannot.