Renewable energy sources like wind and solar irradiance are essential for addressing global energy demands and environmental challenges. However, their inherent variability and intermittency pose significant difficulties in forecasting and grid integration, demanding advanced predictive models. This book proposes fractional-order neural networks and fractional-order LSTM models to enhance prediction accuracy and address challenges related to incomplete data. For wind energy forecasting, single and multi-layer FONNFractional-Order Neural Network (FONN) architectures have been developed using datasets from Texas wind turbines and Jeju Island wind farms, employing both conventional and fractional activation functions. The Levenberg-Marquardt algorithm has been used to train FONNFractional-Order Neural Network (FONN) models, and their performance has been evaluated using metrics such as Mean Square Error and Coefficient of Determination. The LSTM and Bidirectional LSTM (Bi-LSTM) models have been employed to address incomplete data issues from sensor or communication errors, optimize hyperparameters, and train using the Adam solver. Furthermore, the FOLSTM model has been implemented to forecast solar irradiance.