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

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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
    División de Ingeniería, Instituto Tecnológico y de Estudios Superiores de Monterrey, Monterrey 64849, Nuevo León, Mexico)

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.

Suggested Citation

  • Vicente Borja-Jaimes & Jorge Salvador Valdez-Martínez & Miguel Beltrán-Escobar & Alan Cruz-Rojas & Alfredo Gil-Velasco & Antonio Coronel-Escamilla, 2025. "A Review of Fractional Order Calculus Applications in Electric Vehicle Energy Storage and Management Systems," Mathematics, MDPI, vol. 13(18), pages 1-31, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:18:p:2920-:d:1745728
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