  Foresight of CO$_2$ emissions from fuel combustion is essential for
policy-makers to identify ready targets for effective reduction plans and
further to improve energy policies and plans. For the purpose of accurately
forecasting the future development of China's CO$_2$ emissions from fuel
combustion, a novel continuous fractional nonlinear grey Bernoulli model is
developed in this paper. The fractional nonlinear grey Bernoulli model already
in place is known that has a fixed first-order derivative that impairs the
predictive performance to some extent. To address this problem, in the newly
proposed model, a flexible variable is introduced into the order of derivative,
freeing it from integer-order accumulation. In order to further improve the
performance of the newly proposed model, a meta-heuristic algorithm, namely
Grey Wolf Optimizer (GWO), is determined to the emerging coefficients. To
demonstrate the effectiveness, two real examples and China's fuel
combustion-related CO$_2$ emissions are used for model validation by comparing
with other benchmark models, the results show the proposed model outperforms
competitors. Thus, the future development trend of fuel combustion-related
CO$_2$ emissions by 2023 are predicted, accounting for 10039.80 Million tons
(Mt). In accordance with the forecasts, several suggestions are provided to
curb carbon dioxide emissions.
