The Hausdorff dimension of Hadamard fractional integral of a fractal function
Kui Yao, Kunyuan Li, Zekun Wang, He Ming
Abstract
This paper mainly investigates the Hadamard fractional integral of the generalized Weierstrass function with random phases. We get the Hausdorff dimension of this type of fractal function by using potential theory and some classical methods. We show that there exists a linear connection between the Hausdorff dimension of this fractal function and the order of Hadamard fractional integral.
Topics & Concepts
MathematicsHadamard transformHausdorff dimensionFractalFractal dimensionFractal dimension on networksMinkowski–Bouligand dimensionMathematical analysisHadamard three-lines theoremDimension functionPure mathematicsEffective dimensionFractional calculusHausdorff measureFractal analysisHadamard matrixAdvanced Mathematical Theories and ApplicationsMathematical Dynamics and FractalsChaos control and synchronization