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The Effect Of The Weyl Fractional Integral On Functions

Author

Listed:
  • XIA TING

    (Productivity Centre of JiangSu Province, Nanjing 210042, P. R. China)

  • CHEN LEI

    (Information Engineering University, ZhengZhou 450001, P. R. China)

  • LUO LING

    (PLA Army Engineering University, Nanjing 211101, P. R. China)

  • WANG YONG

    (PLA Army Engineering University, Nanjing 211101, P. R. China)

Abstract

This paper mainly discusses the influence of the Weyl fractional integrals on continuous functions and proves that the Weyl fractional integrals can retain good properties of many functions. For example, a bounded variation function is still a bounded variation function after the Weyl fractional integral. Continuous functions that satisfy the Holder condition after the Weyl fractional integral still satisfy the Holder condition, furthermore, there is a linear relationship between the order of the Holder conditions of the two functions. At the end of this paper, the classical Weierstrass function is used as an example to prove the above conclusion.

Suggested Citation

  • Xia Ting & Chen Lei & Luo Ling & Wang Yong, 2021. "The Effect Of The Weyl Fractional Integral On Functions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-5, December.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:08:n:s0218348x21502753
    DOI: 10.1142/S0218348X21502753
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    Cited by:

    1. Sara Contreras-Martos & Alfonso Leiva & Álvaro Sanchez & Emma Motrico & Juan Bellón & Susana Aldecoa Landesa & Rosa Magallón-Botaya & Marc Casajuana-Closas & Edurne Zabaleta-del-Olmo & Bonaventura Bol, 2021. "Implementation of the EIRA 3 Intervention by Targeting Primary Health Care Practitioners: Effectiveness in Increasing Physical Activity," IJERPH, MDPI, vol. 18(19), pages 1-16, October.

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