WHAT IS THE EFFECT OF THE WEYL FRACTIONAL INTEGRAL ON THE HÖLDER CONTINUOUS FUNCTIONS?

Xiaojun Cui, Wei Xiao

2020Fractals10 citationsDOI

Abstract

Let [Formula: see text] be [Formula: see text]-Hölder continuous on [Formula: see text] and well-defined about the Weyl fractional integral. Then, [Formula: see text] where [Formula: see text] and [Formula: see text]. This estimation shows that the Box dimension of [Formula: see text] leads to some similar linear dimension decrease like the Riemann–Liouville fractional integral [Y. S. Liang and W. Y. Su, Fractal dimensions of fractional integral of continuous functions, Acta Math. Sin. 32 (2016) 1494–1508].

Topics & Concepts

MathematicsDimension (graph theory)Fractional calculusFractal dimensionHölder conditionPure mathematicsFractalMathematical analysisMathematical Dynamics and FractalsFractional Differential Equations SolutionsMathematical and Theoretical Analysis