A Review of Fractional Order Calculus Applications in Electric Vehicle Energy Storage and Management Systems

Vicente Borja-Jaimes (), Jorge Salvador Valdez-Martínez, Miguel Beltrán-Escobar, Alan Cruz-Rojas, Alfredo Gil-Velasco and Antonio Coronel-Escamilla ()
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Vicente Borja-Jaimes: Departamento de Ingeniería Electrónica, Centro Nacional de Investigación y Desarrollo Tecnológico (CENIDET), Tecnológico Nacional de México, Interior Internado Palmira s/n, Palmira, Cuernavaca 62490, Morelos, Mexico
Jorge Salvador Valdez-Martínez: División Académica de Mecánica Industrial, Universidad Tecnológica Emiliano Zapata del Estado de Morelos, Av. Universidad Tecnológica No. 1, Emiliano Zapata 62760, Morelos, Mexico
Miguel Beltrán-Escobar: División Académica de Mecánica Industrial, Universidad Tecnológica Emiliano Zapata del Estado de Morelos, Av. Universidad Tecnológica No. 1, Emiliano Zapata 62760, Morelos, Mexico
Alan Cruz-Rojas: Departamento de Ciencias Computacionales e Ingenierías, Centro Universitario de los Valles, Universidad de Guadalajara, Ameca 46600, Jalisco, Mexico
Alfredo Gil-Velasco: Dirección Académica de la Ingeniería en Tecnologías de la Información y la Ingeniería en Electrónica y Telecomunicaciones, Universidad Politécnica del Estado de Morelos, Jiutepec 62550, Morelos, Mexico
Antonio Coronel-Escamilla: División Académica de Mecánica Industrial, Universidad Tecnológica Emiliano Zapata del Estado de Morelos, Av. Universidad Tecnológica No. 1, Emiliano Zapata 62760, Morelos, Mexico

Mathematics, 2025, vol. 13, issue 18, 1-31

Abstract: Fractional-order calculus (FOC) has gained significant attention in electric vehicle (EV) energy storage and management systems, as it provides enhanced modeling and analysis capabilities compared to traditional integer-order approaches. This review presents a comprehensive survey of recent advancements in the application of FOC to EV energy storage systems, including lithium-ion batteries (LIBs), supercapacitors (SCs), and fuel cells (FCs), as well as their integration within energy management systems (EMS). The review focuses on developments in electrochemical, equivalent circuit, and data-driven models formulated in the fractional-order domain, which improve the representation of nonlinear, memory-dependent, and multi-scale dynamics of energy storage devices. It also discusses the benefits and limitations of current FOC-based models, identifies open challenges such as computational feasibility and parameter identification, and outlines future research directions. Overall, the findings indicate that FOC offers a robust framework with significant potential to advance next-generation EV energy storage and management systems.

Keywords: fractional-order calculus; electrical vehicles; energy storage system; energy management system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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