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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.

PM10 is one of the most dangerous air pollutants which is harmful to the ecological system and human health. Accurate forecasting of PM10 concentration makes it easier for the government to make efficient decisions and policies. However, the PM10 concentration, particularly, the emerging short-term concentration has high uncertainties as it is often impacted by many factors and also time varying. Above all, a new methodology which can overcome such difficulties is needed.

The grey system theory is used to build the short-term PM10 forecasting model. The Euler polynomial is used as a driving term of the proposed grey model, and then the convolutional solution is applied to make the new model computationally feasible. The grey wolf optimizer is used to select the optimal nonlinear parameters of the proposed model.

The introduction of the Euler polynomial makes the new model more flexible and more general as it can yield several other conventional grey models under certain conditions. The new model presents significantly higher performance, is more accurate and also more stable, than the six existing grey models in three real-world cases and the case of short-term PM10 forecasting in Tianjin China.

With high performance in the real-world case in Tianjin China, the proposed model appears to have high potential to accurately forecast the PM10 concentration in big cities of China. Therefore, it can be considered as a decision-making support tool in the near future.

This is the first work introducing the Euler polynomial to the grey system models, and a more general formulation of existing grey models is also obtained. The modelling pattern used in this paper can be used as an example for building other similar nonlinear grey models. The practical example of short-term PM10 forecasting in Tianjin China is also presented for the first time.

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.

This study analyses the relationship between the networks of business incubators (BIs) and new venture performance. It proposes an integrated model for identifying the influence of BIs' internal and external networks on new venture performance through the entrepreneurial orientation (EO) and environmental dynamism.

The study uses multiple regression analysis on a sample of 205 new ventures in Chinese BIs.

Both the internal and external networks of BIs positively affect new venture performance and EO has a mediating effect in this relationship. Environmental dynamism plays a positive moderating role in the relationship between BIs' internal and external networks and EO.

Based on the results of this study, incubator managers should focus on creating internal and external networks and leveraging network embeddedness to influence new venture performance. Further, new ventures should focus on strengthening their EO and fully consider the impact of environmental dynamism on EO implementation.

To address the research gaps in understanding how BI networks can support new venture growth, this study integrates BIs' internal and external networks and explores their impacts on new venture performance using co-production theory and the resource-based view. It thus opens the black box on how BI's networks affect performance from the EO perspective. Moreover, this study fully clarifies chain relationships by identifying and analysing the moderating role of environmental dynamism.

Previous studies have shown that the application of information technology (IT) can help break through the innovation boundaries of firms and has undoubtedly become a key enabler of collaborative innovation. These studies, however, are mainly based on theoretical analysis and case studies, and little is empirically known about the relationship between IT investments and collaborative innovation. Therefore, the purpose of this study is to empirically explore how firms' IT investments affect the firms' collaborative innovation performance. The authors also examine the moderating roles of the top management team's (TMT's) educational background and absorptive capacity in this relationship.

The authors collected data on 2,097 listed Chinese manufacturing companies and used the ordinary least squares (OLS) method to perform regression analysis. In addition, the authors conducted robustness tests using the propensity score matching (PSM) method and the instrumental variable method.

The results show that the relationship between IT investments and collaborative innovation is inverted, U-shaped and curvilinear. In addition, the TMT's educational background and absorptive capacity positively moderate the inverted U-shaped relationship between IT investments and collaborative innovation.

The study's findings on the relationship between IT investments and collaborative innovation differ from previous mainstream findings that recognized a positive linear relationship. The authors' findings deepen the understanding of the dual role of IT investments. Moreover, this research helps expand the contingency perspective in IT investments and collaborative innovation research.

As social networking sites (SNSs) gain popularity, they are being widely used by entrepreneurs to obtain social capital to carry out business ventures. However not all SNS usage behaviors promote entrepreneurship. Only when individuals actively participate in SNSs relationship maintenance behaviors they can obtain resources that are conducive to promoting social entrepreneurship. The aim of this study is to explore the role of WeChat relationship maintenance behavior (WRMB) on social entrepreneurial intention (SEI) with dual narcissism as an essential antecedent that affects SNS use.

Based on dual narcissism theory and the theoretical framework that networking is a critical skill and activity for the success of social entrepreneurship, this study proposes a serial mediation model that explores the formation of SEI. This study collected data from a sample of 275 MBA students in China and applied multiple regression and confirmatory factor analysis techniques to test the research model.

The results reveal narcissistic admiration (NA) is positively associated with WRMB, while narcissistic rivalry (NR) is negatively associated with such behavior. And the positive impact of NA on SEI can be explained by WRMB and social capital paths, while the negative impact of NR cannot.

This research is the first application of dual narcissism in the field of SEI, which provides a new way to explain the antecedents of SEI under the social network. The findings provide an effective reference path for social entrepreneurship education in universities and educational institutions and enlighten the correct distinction between dual narcissism in entrepreneurial psychological consultation.

Based on a personality-behavior-outcome framework, this study analyzes how entrepreneurs' dual narcissism (i.e. narcissistic admiration and rivalry) affects new venture growth (NVG) through learning from entrepreneurial failure (LFEF) and discusses the moderating effect of personal initiative on the relationship between dual narcissism and LFEF.

A total of 294 entrepreneurs from different cities and industries in China were selected as the research sample. The mediation effect was examined using the PROCESS macro, and the moderation effect was tested via hierarchical regression analysis.

This study found that narcissistic admiration positively affected NVG, while narcissistic rivalry had the opposite effect. LFEF mediated the relationships between narcissistic admiration/rivalry and NVG. In addition, the effects of narcissistic admiration and rivalry on LFEF were moderated by personal initiative.

The findings suggest that entrepreneurs with narcissistic rivalry should deliberately regulate their cognition of failure and strengthen their learning from failure. Moreover, entrepreneurship education mentors should emphasize cultivating and guiding entrepreneurs' personal initiative in the context of frustration education. In addition, venture capitalists can consider incorporating the personality traits (i.e. dual narcissism and personal initiative) of entrepreneurs into the investment decision-making index system.

This study advances the relationship between narcissism and performance through the perspective of dual narcissism and provides a learning theory perspective for analyzing the narcissism–performance relationship. Moreover, by exploring the moderating role of personal initiative, this study enriches the understanding of the conditional factor that affects the ability to learn from failure.

The purpose of this study is to reveal the influence mechanism of social innovation education (SIE) on sustainability learning outcomes and analyze the roles of intrinsic learning motivation and prosocial motivation.

A sample of 322 undergraduates from one higher education institution in Tianjin was used to test the hypotheses.

This study found that SIE positively affected sustainability learning outcomes, and intrinsic learning motivation mediated the relationship between them. The results showed that prosocial motivation positively moderates the positive effect of SIE on intrinsic learning motivation and the overall mediation model.

The findings have important practical implications for higher education institutions to carry out SIE. Higher education institutions should focus on integrating social innovation and sustainability into top-level design. Furthermore, higher education institutions should focus on stimulating students’ intrinsic learning motivation and cultivating their prosocial motivation.

This study identified the relationship between SIE and sustainability learning outcomes and clarified the influence mechanism of SIE on sustainability learning outcomes. Moreover, this study emphasized the importance of prosocial motivation as a key boundary condition of SIE.

This study explores the influence of sharing achievement (i.e. sustainability, enjoyment, and economic benefits) obtained by participating in the sharing economy on social entrepreneurial intention (SEI), as well as the role of perceived social worth and social entrepreneurial self-efficacy (SESE).

This study used multiple regression analysis on a sample of 331 MBA students aged between 24 and 48 years.

The findings indicate that sharing achievement is positively related with SEI, and perceived social worth mediates the relationship between them. Moreover, SESE not only has a moderating effect on the relationship between perceived social worth and SEI but also positively moderates the overall mediation model.

Entrepreneurship educators could focus on improving students' SESE through courses and training. Whereas, policymakers and decision makers should actively promote the sharing economy model and regulate its management. Moreover, existing organizers of the sharing economy should improve participants' sharing achievement.

This study determines the relationship between sharing achievement and SEI and enriches the push/pull theory from the perspective of pull factors in the context of the sharing economy. Moreover, by exploring the mediating effect of perceived social worth and the moderating effect of SESE, the study provides understanding on the influence mechanisms of sharing achievements on SEI.

The study clarifies the relationship between students’ perceptions of university support and heterogeneous entrepreneurial intentions in the Chinese context. It proposes a new construct with the classification of growth- and independence-oriented intentions and examines the moderating role of the Chinese sense of face. This study aims to enrich entrepreneurship education research by incorporating cultural factors.

The study uses a questionnaire survey to examine the research hypotheses. Further, the authors collected data from 374 students from Mainland China and applied a regression analysis.

The study clarifies the positive relationship between perceived university support and growth-oriented/independence-oriented entrepreneurial intentions. Further, it proposes the differences in the moderating role of the Chinese sense of face in the relationships between entrepreneurial self-efficacy and growth- and independence-oriented intentions.

Because of the chosen method, the study results may lack generalizability. Hence, future studies are encouraged to test the proposed hypotheses.

The study results have important implications for entrepreneurship education development.

The study is conducted against the background of the “mass entrepreneurship and innovation” policy in China and combines country-specific characteristics to enrich entrepreneurial education and social entrepreneurship.

This study fulfills the intention to examine the influence of cultural factors on entrepreneurship education and identify the heterogeneous entrepreneurial intentions in a single construct.