Introduction of the fractional order accumulation has made significant contributions to the development of forecasting methods, and fractional grey models play a key role in such new methods. However, the fractional grey models may also be inaccurate in some cases as they do not consider the time delayed effect. To further improve the applicability of the existing fractional grey models, a novel fractional grey model called the fractional time delayed grey model is proposed in this paper. The essence of the fractional time delayed term is discussed, revealing that the fractional time delayed term is essentially a function between the polynomial functions with integer order, which can be more flexible to improve the modelling accuracy. The cutting-edge Grey Wolf Optimizer is introduced to find the optimal value of fractional order. Detailed modelling procedures, including the computational steps and the intelligent optimization algorithm, have been clearly presented. Four real world case studies are used to validate the effectiveness of the proposed model, in comparison with 8 existing grey models. Finally the proposed model is applied to forecast the coal and natural gas consumption of Chongqing China, the results show that the proposed model significantly outperforms the other 8 existing grey models. (C) 2019 Elsevier Ltd. All rights reserved.