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.
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