Fractal dimension of Riemann-Liouville fractional integral of 1-dimensional continuous functions

By Yongshun Liang. Fractional Calculus and Applied Analysis, 2018

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Abstract The present paper investigates fractal dimension of fractional integral of continuous functions whose fractal dimension is 1 on [0, 1]. For any continuous functions whose Box dimension is 1 on [0, 1], Riemann-Liouville fractional integral of these functions of any positive order has been proved to still be 1-dimensional continuous functions on [0, 1].

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b26e13065ab7c89bb923d8f445467e9b0ed2722f