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Further Discussion About Fractional Differentiability Of Certain Continuous Functions

Author

Listed:
  • N. LIU

    (Fundamental Education Department, Army Engineering University of PLA, Nanjing 211101, P. R. China)

  • Y. X. CAO

    (Fundamental Education Department, Army Engineering University of PLA, Nanjing 211101, P. R. China)

  • J. YAO

    (Fundamental Education Department, Army Engineering University of PLA, Nanjing 211101, P. R. China)

Abstract

This paper concentrates on discussing the properties of Riemann–Liouvile fractional (RLF) calculus of two special continuous functions. The first type proves the non-differentiability of a special continuous function that does not satisfy Hölder condition, and the second type uses fractal iteration to construct a fractal function defined on [0, 1] with unbounded variation. Then we calculate RLF integral and RLF derivative of this special function, and give the corresponding numerical calculation results and the corresponding function image.

Suggested Citation

  • N. Liu & Y. X. Cao & J. Yao, 2021. "Further Discussion About Fractional Differentiability Of Certain Continuous Functions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(07), pages 1-12, November.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:07:n:s0218348x21502224
    DOI: 10.1142/S0218348X21502224
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