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Fractional Order Calculus: Basic Concepts and Engineering Applications

Author

Listed:
  • Ricardo Enrique Gutiérrez
  • João Maurício Rosário
  • José Tenreiro Machado

Abstract

The fractional order calculus (FOC) is as old as the integer one although up to recently its application was exclusively in mathematics. Many real systems are better described with FOC differential equations as it is a well-suited tool to analyze problems of fractal dimension, with long-term “memory†and chaotic behavior. Those characteristics have attracted the engineers' interest in the latter years, and now it is a tool used in almost every area of science. This paper introduces the fundamentals of the FOC and some applications in systems' identification, control, mechatronics, and robotics, where it is a promissory research field.

Suggested Citation

  • Ricardo Enrique Gutiérrez & João Maurício Rosário & José Tenreiro Machado, 2010. "Fractional Order Calculus: Basic Concepts and Engineering Applications," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-19, May.
    • Handle: RePEc:hin:jnlmpe:375858
    DOI: 10.1155/2010/375858
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    Cited by:

    1. Asmae Tajani & Fatima-Zahrae El Alaoui, 2023. "Boundary Controllability of Riemann–Liouville Fractional Semilinear Evolution Systems," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 767-780, August.
    2. Fiuzy, Mohammad & Shamaghdari, Saeed, 2023. "Robust H∞-PID control Stability of fractional-order linear systems with Polytopic and two-norm bounded uncertainties subject to input saturation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 550-581.
    3. Eva-Henrietta Dulf, 2019. "Simplified Fractional Order Controller Design Algorithm," Mathematics, MDPI, vol. 7(12), pages 1-21, December.
    4. Pan Mu & Lei Wang & Chongyang Liu, 2020. "A Control Parameterization Method to Solve the Fractional-Order Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 187(1), pages 234-247, October.
    5. Wang, Yujie & Li, Mince & Chen, Zonghai, 2020. "Experimental study of fractional-order models for lithium-ion battery and ultra-capacitor: Modeling, system identification, and validation," Applied Energy, Elsevier, vol. 278(C).
    6. Gayathri Vivekanandan & Mahtab Mehrabbeik & Hayder Natiq & Karthikeyan Rajagopal & Esteban Tlelo-Cuautle, 2022. "Fractional-Order Memristive Wilson Neuron Model: Dynamical Analysis and Synchronization Patterns," Mathematics, MDPI, vol. 10(16), pages 1-9, August.

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