Further discussion about fractional differentiability of certain continuous functions. (English) Zbl 1489.26007
Summary: 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.
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