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Numerical Approaches to Fractional Integrals and Derivatives: A Review

Author

Listed:
  • Min Cai

    (Department of Mathematics, Shanghai University, Shanghai 200444, China)

  • Changpin Li

    (Department of Mathematics, Shanghai University, Shanghai 200444, China)

Abstract

Fractional calculus, albeit a synonym of fractional integrals and derivatives which have two main characteristics—singularity and nonlocality—has attracted increasing interest due to its potential applications in the real world. This mathematical concept reveals underlying principles that govern the behavior of nature. The present paper focuses on numerical approximations to fractional integrals and derivatives. Almost all the results in this respect are included. Existing results, along with some remarks are summarized for the applied scientists and engineering community of fractional calculus.

Suggested Citation

  • Min Cai & Changpin Li, 2020. "Numerical Approaches to Fractional Integrals and Derivatives: A Review," Mathematics, MDPI, vol. 8(1), pages 1-53, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:43-:d:304161
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    References listed on IDEAS

    as
    1. Fausto Ferrari, 2018. "Weyl and Marchaud Derivatives: A Forgotten History," Mathematics, MDPI, vol. 6(1), pages 1-25, January.
    2. Zhang, Yuxin & Li, Qian & Ding, Hengfei, 2018. "High-order numerical approximation formulas for Riemann-Liouville (Riesz) tempered fractional derivatives: construction and application (I)," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 432-443.
    3. Osama Moaaz & Dimplekumar Chalishajar & Omar Bazighifan, 2019. "Some Qualitative Behavior of Solutions of General Class of Difference Equations," Mathematics, MDPI, vol. 7(7), pages 1-12, July.
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    Cited by:

    1. Ashish Rayal & Bhagawati Prasad Joshi & Mukesh Pandey & Delfim F. M. Torres, 2023. "Numerical Investigation of the Fractional Oscillation Equations under the Context of Variable Order Caputo Fractional Derivative via Fractional Order Bernstein Wavelets," Mathematics, MDPI, vol. 11(11), pages 1-22, May.
    2. Tuan Anh Bui & Jun-Sik Kim & Junyoung Park, 2023. "Efficient Method for Derivatives of Nonlinear Stiffness Matrix," Mathematics, MDPI, vol. 11(7), pages 1-20, March.

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