The integration of renewable energy sources into electricity markets presents significant challenges due to the inherent variability and uncertainty of power generation from wind, solar, and other renewables. Accurate forecasting is crucial for ensuring grid stability, optimizing market operations, and minimizing economic risks. This paper introduces a hybrid forecasting framework incorporating fractional-order statistical models, fractal-based feature engineering, and deep learning architectures to improve renewable energy forecasting accuracy. Fractional autoregressive integrated moving average (FARIMA) and fractional exponential smoothing (FETS) models are explored for capturing long-memory dependencies in energy time-series data. Additionally, multifractal detrended fluctuation analysis (MFDFA) is used to analyze the intermittency of renewable energy generation. The hybrid approach further integrates wavelet transforms and convolutional long short-term memory (CNN-LSTM) networks to model short- and long-term dependencies effectively. Experimental results demonstrate that fractional and fractal-based hybrid forecasting techniques significantly outperform traditional models in terms of accuracy, reliability, and adaptability to energy market dynamics. This research provides insights for market participants, policymakers, and grid operators to develop more robust forecasting frameworks, ensuring a more sustainable and resilient electricity market.

The increasing integration of renewable energy resources and active distribution networks has significantly increased the complexity of optimal power flow (OPF) problems in integrated transmission-distribution (T&D) power systems. To address these challenges, this paper proposes a novel tri-swarm adaptive hybrid optimizer (TAHO) that integrates particle swarm optimization (PSO), grey wolf optimizer (GWO), and jellyfish search (JS) within a unified adaptive optimization framework. The proposed method effectively balances exploration and exploitation to improve convergence stability and optimization accuracy. A multi-objective OPF model is developed to minimize generation cost, power loss, and voltage deviation under operational constraints. Experimental results on integrated IEEE 30-bus and IEEE 33-bus systems demonstrate that the proposed TAHO achieves superior performance with the minimum fitness value of 0.0008, faster convergence within 75 iterations, and the lowest standard deviation of 0.0005 compared with PSO, GWO, and JS. Benchmark evaluations further confirm the robustness and strong global search capability of the proposed framework for renewable-integrated smart grid optimization and real-time OPF applications.

The integration of renewable energy sources into modern power systems introduces stability and resilience challenges due to their intermittent and stochastic behavior. To address these issues, this study proposes an artificial intelligence (AI)-driven statistical complex network (AI-SCN) framework for stability assessments in renewable-integrated power grids. The framework models the grid as a weighted complex network, where the nodes represent generation, storage, and load units, and the edges capture electrical and statistical dependencies. By integrating network topology metrics with data-driven AI models, AI-SCN enables accurate stability margin estimation and resilience quantification under varying renewable penetration levels. Simulations on the Institute of Electrical and Electronics Engineers (IEEE) 39-bus and IEEE 118-bus systems show that AI-SCN outperforms conventional and long short-term memory (LSTM)-based approaches, achieving root mean square error (RMSE) values of 0.0185 and 0.0219, respectively, representing improvements of 40.7% and 58.9%. Furthermore, recovery time is reduced from 12.8 s to 8.4 s, demonstrating the system's enhanced recovery efficiency. These results confirm that AI-SCN offers a scalable and adaptive framework for improving stability and resilience in renewable-dominant power systems.

The increasing complexity of modern networks, from communication infrastructures to power grids and social networks, demands models that capture both structural dependencies and nonlinear dynamics of long memory. We proposed a hybrid framework that unified deep learning (graph neural networks, recurrent/attention modules) with fractional calculus to model nonlocal memory, anomalous diffusion, and self-similarity. Fractional differential formulations provide a principled description of network evolution, for which we stated a checkable stability condition; the learning pipeline coupled gradient-based training with fractional operators for robust, interpretable prediction. On Los Angeles metropolitan area traffic (METR-LA) dataset, the proposed ensemble integrated deep fractional model (EIDFM) achieved mean absolute error (MAE) around 6.4 and root mean square error (RMSE) 10.8, which showed improvement over the strongest baseline hybrid (CNN-LSTM): MAE $7.8$, RMSE $12.5$) by 18% and 14%, respectively; mean absolute percentage error (MAPE) droped from $6.3\mathrm{\%}$ to $5.2\mathrm{\%}$ ( $\approx 17\mathrm{\%}$ relative), while $R^2$ rose from $0.91$ to $0.94$. Results were reported as mean $\pm$std over five seeds with paired significance tests. A lightweight efficiency analysis showed modest overhead relative to the baseline (inference $3.2\pm 0.3$ ms/step vs. $2.8\pm 0.2$; parameters $12.8$M vs. $11.3$M), justified by the accuracy gains. These findings indicated that integrating fractional operators with graph-based deep learners yielded a mathematically grounded and practically effective paradigm for understanding and managing complex network dynamics.