Fractional integrals of the Weierstrass functions: the exact box dimension. (English) Zbl 1062.28013
Summary: The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The exact box dimension for such functions for many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.
MSC:
| 28A80 | Fractals |
| 28A78 | Hausdorff and packing measures |
| 26A27 | Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives |
| 26A33 | Fractional derivatives and integrals |
Keywords:
Riemann-Liouville fractional integral; fractal; fractional calculus; Weierstrass function; box dimension; Hausdorff dimensionReferences:
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