FURTHER DISCUSSION ABOUT FRACTIONAL DIFFERENTIABILITY OF CERTAIN CONTINUOUS FUNCTIONS

N. Liu, Y. X. Cao and J. Yao
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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

FRACTALS (fractals), 2021, vol. 29, issue 07, 1-12

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.

Keywords: Lipschitz Condition; Unbounded Variation; Fractal Dimension; Fractional Calculus (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21502224

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