The prediction of the tertiary industry's output value is essential for enhancing the market economic system and providing guidance for the government in formulating relevant economic policies. The tertiary industry encompasses various sectors such as finance and transportation, and its total output value exhibits uncertain and nonlinear trends. Triangular fuzzy number sequences contain more comprehensive information than exact number sequences. Therefore, a nonlinear grey Bernoulli model with conformable fractional accumulation for triangular fuzzy sequences is proposed. Firstly, the conformable fractional accumulation generating operation is utilized to mitigate the volatility tendency of the original sequences. Additionally, a time power function term is introduced to capture the power exponential trend. Furthermore, an improved whale optimization algorithm incorporating opposition-based learning strategy and adaptive control parameters is employed to optimize the model parameters, which has been verified through algorithm comparison experiments. Three existing grey models are used as competing models to validate the prediction accuracy of our proposed model. Finally, we utilize this proposed model to predict the tertiary industry's output values in both Yangtze and Pearl River Deltas for 2024–2026.