SAID SHEHATA

Renewable energy microgrids exhibit memory-dependent, nonlinear, and multi-timescale dynamics that classical integer-order methods cannot adequately represent. Fractional calculus extends differentiation and integration to non-integer orders, providing a rigorous framework for capturing hereditary effects, anomalous diffusion, and long-range dependence across microgrid subsystems. Despite growing research activity, existing reviews address isolated topics without a unified treatment spanning all major application domains. This survey organizes fractional-order methodologies within a two-domain framework — fractional-order control and integrated fractional calculus-based methods — spanning five technical categories: component modeling, hierarchical control, optimization, forecasting, and validation. Fractional-order equivalent circuit models with constant phase elements are reviewed for state-of-charge and state-of-health estimation in electrochemical storage and photovoltaic systems. Fractional-order control schemes, encompassing single-loop and cascade topologies, optimized by metaheuristic methods, exhibit reliable improvements in transient response and robustness compared to integer-order designs. Fractional grey models, FARIMA formulations, and hybrid fractional machine-learning architectures are assessed for renewable generation and load forecasting. Three standardized case studies provide quantitative cross-domain comparisons under consistent conditions. Identified deployment barriers include fractional operator computational cost, absent tuning protocols, and limited hardware validation, motivating future research in physics-informed fractional learning, digital twin integration, and edge computing. This survey provides researchers and practitioners with a unified reproducible framework for applying fractional-order techniques in next-generation renewable energy microgrids.

Renewable energy microgrids exhibit memory-dependent, nonlinear, and multi-timescale dynamics that classical integer-order methods cannot adequately represent. Fractional calculus extends differentiation and integration to non-integer orders, providing a rigorous framework for capturing hereditary effects, anomalous diffusion, and long-range dependence across microgrid subsystems. Despite growing research activity, existing reviews address isolated topics without a unified treatment spanning all major application domains. This survey organizes fractional-order methodologies within a two-domain framework — fractional-order control and integrated fractional calculus-based methods — spanning five technical categories: component modeling, hierarchical control, optimization, forecasting, and validation. Fractional-order equivalent circuit models with constant phase elements are reviewed for state-of-charge and state-of-health estimation in electrochemical storage and photovoltaic systems. Fractional-order control schemes, encompassing single-loop and cascade topologies, optimized by metaheuristic methods, exhibit reliable improvements in transient response and robustness compared to integer-order designs. Fractional grey models, FARIMA formulations, and hybrid fractional machine-learning architectures are assessed for renewable generation and load forecasting. Three standardized case studies provide quantitative cross-domain comparisons under consistent conditions. Identified deployment barriers include fractional operator computational cost, absent tuning protocols, and limited hardware validation, motivating future research in physics-informed fractional learning, digital twin integration, and edge computing. This survey provides researchers and practitioners with a unified reproducible framework for applying fractional-order techniques in next-generation renewable energy microgrids.

Renewable energy microgrids exhibit memory-dependent, nonlinear, and multi-timescale dynamics that classical integer-order methods cannot adequately represent. Fractional calculus extends differentiation and integration to non-integer orders, providing a rigorous framework for capturing hereditary effects, anomalous diffusion, and long-range dependence across microgrid subsystems. Despite growing research activity, existing reviews address isolated topics without a unified treatment spanning all major application domains. This survey organizes fractional-order methodologies within a two-domain framework — fractional-order control and integrated fractional calculus-based methods — spanning five technical categories: component modeling, hierarchical control, optimization, forecasting, and validation. Fractional-order equivalent circuit models with constant phase elements are reviewed for state-of-charge and state-of-health estimation in electrochemical storage and photovoltaic systems. Fractional-order control schemes, encompassing single-loop and cascade topologies, optimized by metaheuristic methods, exhibit reliable improvements in transient response and robustness compared to integer-order designs. Fractional grey models, FARIMA formulations, and hybrid fractional machine-learning architectures are assessed for renewable generation and load forecasting. Three standardized case studies provide quantitative cross-domain comparisons under consistent conditions. Identified deployment barriers include fractional operator computational cost, absent tuning protocols, and limited hardware validation, motivating future research in physics-informed fractional learning, digital twin integration, and edge computing. This survey provides researchers and practitioners with a unified reproducible framework for applying fractional-order techniques in next-generation renewable energy microgrids.

Renewable energy microgrids exhibit memory-dependent, nonlinear, and multi-timescale dynamics that classical integer-order methods cannot adequately represent. Fractional calculus extends differentiation and integration to non-integer orders, providing a rigorous framework for capturing hereditary effects, anomalous diffusion, and long-range dependence across microgrid subsystems. Despite growing research activity, existing reviews address isolated topics without a unified treatment spanning all major application domains. This survey organizes fractional-order methodologies within a two-domain framework — fractional-order control and integrated fractional calculus-based methods — spanning five technical categories: component modeling, hierarchical control, optimization, forecasting, and validation. Fractional-order equivalent circuit models with constant phase elements are reviewed for state-of-charge and state-of-health estimation in electrochemical storage and photovoltaic systems. Fractional-order control schemes, encompassing single-loop and cascade topologies, optimized by metaheuristic methods, exhibit reliable improvements in transient response and robustness compared to integer-order designs. Fractional grey models, FARIMA formulations, and hybrid fractional machine-learning architectures are assessed for renewable generation and load forecasting. Three standardized case studies provide quantitative cross-domain comparisons under consistent conditions. Identified deployment barriers include fractional operator computational cost, absent tuning protocols, and limited hardware validation, motivating future research in physics-informed fractional learning, digital twin integration, and edge computing. This survey provides researchers and practitioners with a unified reproducible framework for applying fractional-order techniques in next-generation renewable energy microgrids.

Background: Egypt is one of the top steel producers in the Middle East and Africa, yet it faces acute water scarcity and rising energy costs, making it a critical context for studying trade-offs among carbon emissions, water ecological effects, and operational cost in steel supply chain. Methods: Using a multi-objective optimization model based on real data from a major Egyptian steel manufacturer, this study evaluates trade-offs among cost, tardiness, and environmental impact measured by carbon emissions and water ecological effects. Unlike prior studies, this study demonstrates that dedicated warehousing enables batch-level traceability of returned scrap while reducing material handling travel time and carbon emissions. The AUGMECON method generates Pareto-optimal solutions, and sensitivity analysis is conducted on six parameters: scrap take-back rate, demand variability, raw material price, energy cost, production capacity, and carbon tax. Results: Demand and raw material prices dominate performance: a 5% demand increase raises cost by 8.6%, and a 15% raw material price increase raises cost by 32.7%. The knee-point solution achieves 58.18 billion EGP, 0.99 months tardiness, and 2096 million kg CO2 over nine months. Conclusions: This study quantifies the impact of the circular economy and operational parameters on steel supply chain performance under a dedicated warehousing policy.

Background: Egypt is one of the top steel producers in the Middle East and Africa, yet it faces acute water scarcity and rising energy costs, making it a critical context for studying trade-offs among carbon emissions, water ecological effects, and operational cost in steel supply chain. Methods: Using a multi-objective optimization model based on real data from a major Egyptian steel manufacturer, this study evaluates trade-offs among cost, tardiness, and environmental impact measured by carbon emissions and water ecological effects. Unlike prior studies, this study demonstrates that dedicated warehousing enables batch-level traceability of returned scrap while reducing material handling travel time and carbon emissions. The AUGMECON method generates Pareto-optimal solutions, and sensitivity analysis is conducted on six parameters: scrap take-back rate, demand variability, raw material price, energy cost, production capacity, and carbon tax. Results: Demand and raw material prices dominate performance: a 5% demand increase raises cost by 8.6%, and a 15% raw material price increase raises cost by 32.7%. The knee-point solution achieves 58.18 billion EGP, 0.99 months tardiness, and 2096 million kg CO2 over nine months. Conclusions: This study quantifies the impact of the circular economy and operational parameters on steel supply chain performance under a dedicated warehousing policy.