Abstract:
In this paper it is proved that localized fractional derivatives of Riemann – Liouville type of order 0 < $\alpha$ < 1 are bounded from the Hölder space with exponent $\lambda$, 0 < $\lambda$ \le 1 and logarithmic factor into the Hölder space with exponent $\lambda$ - $\alpha$, 0 < $\lambda$ - $\alpha$ and logarithmic factor. Localized and local fractional derivatives, minimum and maximum points of the Takagi function are calculated. It is shown that the Takagi function belongs to the Hölder space with exponent one and logarithmic factor.
Keywords:localized fractional derivative, local fractional derivative, takagi function.
