On a linearity between fractal dimension and order of fractional calculus in Hölder space

摘要

In this paper, the linear relationship between fractal dimensions and the order of fractional calculus of functions in Hölder space has been mainly investigated. Under specific Hölder condition, the linear connection between Box dimension and the order of Riemann-Liouville fractional integral and derivative has been proved. This linear connection is also established with K-dimension and Packing dimension. Some function examples have been given in the end.