4.6 Article

Analysis of fractal dimension of mixed Riemann-Liouville integral

期刊

NUMERICAL ALGORITHMS
卷 91, 期 3, 页码 1021-1046

出版社

SPRINGER
DOI: 10.1007/s11075-022-01290-2

关键词

Box dimension; Hausdorff dimension; Riemann-Liouville fractional integral; Holder condition; Bounded variation

资金

  1. CSIR, India [09/1058(0012)/2018-EMR-I]

向作者/读者索取更多资源

In this article, we provide a rigorous study on the fractal dimension of the graph of the mixed Riemann-Liouville fractional integral for various choices 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 discuss the cases of two-dimensional continuous functions and unbounded variational continuous functions, giving corresponding results.
In this article, we provide a rigorous study on the fractal dimension of the graph of the mixed Riemann-Liouville fractional integral for various choices 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 the 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 two. Moreover, we illustrate our results by using some examples.

作者

我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。

评论

主要评分

4.6
评分不足

次要评分

新颖性
-
重要性
-
科学严谨性
-
评价这篇论文

推荐

暂无数据
暂无数据