BOX DIMENSION OF HADAMARD FRACTIONAL INTEGRAL OF CONTINUOUS FUNCTIONS OF BOUNDED AND UNBOUNDED VARIATION

作者：Wu, Xiao Er^*; Du, Jun Huai

来源：Fractals-Complex Geometry Patterns and Scaling in Nature and Society, 2017, 25(3): 1750035.

DOI：10.1142/S0218348X17500359

• Fractal Dimension
• Bounded Variation
• Unbounded Variation
• Hadamard Fractional Integral

The present paper investigates fractal dimension of Hadamard fractional integral of continuous functions of bounded and unbounded variation. It has been proved that Hadamard fractional integral of continuous functions of bounded variation still is continuous functions of bounded variation. Definition of an unbounded variation point has been given. We have proved that Box dimension and Hausdorff dimension of Hadamard fractional integral of continuous functions of bounded variation are 1. In the end, Box dimension and Hausdorff dimension of Hadamard fractional integral of certain continuous functions of unbounded variation have also been proved to be 1.

• 出版日期2017-6
• 单位南京理工大学