AI 中文总结
本研究提出带时延的分数阶能源供需模型，结合GL离散化方案，经理论分析与数值验证，为现实能源预测提供灵活框架，支撑能源政策与管理，还为后续研究奠定基础。
AI 中文摘要
为表征当代能源系统的复杂动力学，本研究提出了一种新型带时延的分数阶能源供需模型。与传统整数阶模型相比，该分数阶模型自然适配记忆效应和遗传效应，时延分量的引入则考虑了能源生产、传输和消费中不可避免的滞后。为确保所提模型的数学严谨性，我们证明了解的存在性与唯一性；还在Ulam-Hyers概念框架下研究了模型的稳定性，证明其对微小不确定性和扰动具有鲁棒性。为处理时延系统的分数阶导数，我们采用Grnwald-Letnikov（GL）离散化方案，该方案为近似求解提供了简便有效的方法。通过数值研究时延参数和分数阶阶次对系统行为的影响，揭示了它们如何塑造振荡、收敛速率和平衡状态。结果表明，结合GL离散化方案的带时延分数阶建模，为研究能源动力学提供了灵活且现实的框架，该框架为长期政策规划、供应管理和需求预测提供了重要见解，还为后续融入优化技术、随机效应及可再生能源整合奠定了基础，将进一步推动高效可持续能源系统的发展。我们还讨论了三种敏感性分析场景：高需求与低供应结合、高可再生能源占比且进口减少、低需求且高进口，结果显示这些场景下系统表现稳定且高效。
英文摘要
In order to represent the complex dynamics of contemporary energy systems, a novel fractional-order energy supply-demand model with time delay is presented in this investigation. The fractional model, compared to traditional integer-order models, naturally accommodates for memory and genetic effects, and the incorporation of delay component takes into account unavoidable lags in energy production, transmission, and consumption. To ensure the mathematical rigor of the proposed model, we prove the existence and uniqueness of solutions. We additionally examine into the model's stability within the Ulam-Hyers concept and demonstrate that it is resilient to minor uncertainties and perturbations. To handle fractional derivatives with delay systems, we utilize the Grnwald-Letnikov (GL) discretization scheme, which offers a straightforward and effective method for approximating the solutions. The impact of delay parameters and fractional orders on system behavior is investigated numerically, demonstrating how they shape oscillations, convergence rates, and equilibrium states. According to the results, fractional-order modeling with delay, reinforced by the GL discretization scheme, provides a flexible and realistic framework for examining energy dynamics. This framework gives important insights for long-term policy planning, supply management, and demand forecasting. Additionally, the framework lays the groundwork for upcoming additions that incorporate optimization techniques, stochastic effects, and the integration of renewable energy sources, all of which will further the development of effective and sustainable energy systems. We also discuss three sensitivity analysis scenarios including high demand combined with low supply, high renewable and reduced and imports low demand with high imports which the results show stable and efficient results.
