Green Energy Generation Dynamical System: Fractal-Fractional Mathematical Modeling with AI-Driven Data Analysis

Abstract

As the demand for renewable energy increases, it becomes more vital to efficiently integrate different resources such as wind and solar energy. This study illustrates a novel integrated mechanism for analyzing a green energy generation dynamical system utilizing the Fractal-Fractional (FF) sense of operators. We give a robust deep learning framework designed to successfully model the complex interactions and nonlinear characteristics of these energy sources. This mechanism leverages FF-calculus to improve the model's efficiency, incorporating comprehensive error analysis and advanced pattern recognition techniques. Our mathematical analysis confirms the feasibility of both the initial and parametric values of the model, demonstrating its robustness. The existence criteria, uniqueness results, and stability were also confirmed in the theoretical aspect of the work. Computational results show that the proposed hybrid system of energy significantly outperforms traditional solar-only systems, achieving an efficiency improvement of approximately 25% in energy generation. This work not only supports the existing knowledge in renewable energy but also provides a practical approach for optimizing green power generation systems by the use of artificial intelligence as a process innovation