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arXiv · 2105.06648

Analysis of Fractal Dimension of Mixed Riemann-Liouville Fractional Integral

Subhash Chandra·Syed Abbas
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Abstract

In this article, we investigate the fractal dimension of the graph of the mixed Riemann-Liouville fractional integral for various choice of continuous functions on a rectangular region. We estimate bounds for the box dimension and the Hausdorff dimension of the graph of the mixed Riemann-Liouville fractional integral of the functions which belong to the class of continuous functions and the class of Holder continuous functions. We also show that the box dimension of the graph of the mixed Riemann-Liouville fractional integral of two-dimensional continuous functions is also two. Furthermore, we give construction of unbounded variational continuous functions. Later, we prove that the box dimension and the Hausdorff dimension of the graph of the mixed Riemann-Liouville fractional integral of unbounded variational continuous functions are also two.

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BibTeXRIS

Subhash Chandra, Syed Abbas. 2021-05-14. Analysis of Fractal Dimension of Mixed Riemann-Liouville Fractional Integral. https://arxiv.org/abs/2105.06648

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