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Some Notes of the Fractional Integral and Derivatives and Its Applications

Author

Listed:
  • Fen Qin
  • Fuyi Xu
  • Huizeng Qin

Abstract

In this paper, the definitions of the fractional derivative and integrals are given by the neutrix limit. Not only is it consistent with the classical results but also the representations of the fractional derivative and integrals are obtained for (x − a)−k, (x − a)−klnp(x − a), (x − a)−kf(x), and (x − a)−klnp(x − a)f(x), where k, p = 1,2, …, f(x) is the analytic function.

Suggested Citation

  • Fen Qin & Fuyi Xu & Huizeng Qin, 2022. "Some Notes of the Fractional Integral and Derivatives and Its Applications," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:8343530
    DOI: 10.1155/2022/8343530
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    References listed on IDEAS

    as
    1. H. J. Haubold & A. M. Mathai & R. K. Saxena, 2011. "Mittag‐Leffler Functions and Their Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    2. Sun, Zhongfeng & Qin, Huizeng & Li, Aijuan, 2016. "Extension of the partial derivatives of the incomplete beta function for complex values," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 63-71.
    3. H. J. Haubold & A. M. Mathai & R. K. Saxena, 2011. "Mittag-Leffler Functions and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-51, May.
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