Since its reform and opening up, China’s economy has undergone rapid development and has experienced problems such as the overexploitation of resources and the destruction of the ecological environment. To achieve a balance between economic growth and environmental protection and to follow the sustainable development path, China must implement corresponding environmental regulation policies and vigorously encourage enterprises to pursue green technology innovation. In this paper, environmental regulation is divided into command-and-control, market incentive and voluntary participation. Command-and-control environmental regulation is measured using the entropy method and the logarithm of the pollution discharge fee income in each region is used as the measurement index of market-incentive environmental regulations. At the same time, the logarithm of the number of environmental protection proposals planned by the National People’s Congress and the number of environmental protection proposals planned by the CPPCC is used as the measurement index of voluntary participation in environmental regulations. Based on a regression equation of the effects of environmental regulations on green technology innovation, this paper uses the two-step system GMM method to analyze the panel data of industrial enterprises larger than a designated size in 30 provinces, autonomous regions and municipalities in China from 2006 to 2017. Moreover, the paper compares the effects of command-and-control, market-incentive and voluntary participatory environmental regulations on green technology innovation. The empirical results show that command-and-control environmental regulations initially have an inverted U-shaped effect on green technology innovation and market incentive and voluntary participatory environmental regulations have a U-shaped effect on green technology innovation. A comparison of the three environmental regulation policies shows that the effect of command-and-control environmental regulation is more significant.

This study aims to investigate the dynamics of three agents in the emerging business bubble model based on the Mittag–Leffler law pertaining to the piecewise classical derivative and non-singular kernel. By generalizing the business bubble dynamics in terms of fractional operators and the piecewise concept, this study presents a new perspective to the field. The entire set of intervals is partitioned into two piecewise intervals to analyse the classical order and conformable order derivatives of an Atangana–Baleanu operator. The subinterval analysis is critical for removing discontinuities in each sub-partition. The existence and uniqueness of the solution based on a piecewise global derivative are tested for the considered model. The approximate root of the system is determined using the piecewise numerically iterative technique of the Newton polynomial. Under the classical order and non-singular law, the approximate root scheme is applied to the piecewise derivative. The curve representation for the piece-wise globalised system is tested by applying the data for the classical and different conformable orders. This establishes the entire density of each compartment and shows a continuous spectrum instead of discrete dynamics. The concept of this study can also be applied to investigate crossover behaviours or abrupt changes in the dynamics of the values of each market.