论文标题
多元分形插值函数的盒子尺寸和分数积分
Box Dimension and Fractional Integrals of Multivariate Fractal Interpolation Functions
论文作者
论文摘要
在本文中，我们为给定数据点构建了多元分形插值函数，并探讨了与$ [0,1] \ times \ cdots \ cdots \ cdots \ times \ times \ times [0,1] [q \ text {-times {-times}）的存在$α$ fractal函数的存在。选择参数以使相应的分形版本保留一些原始函数的属性，例如，如果给定函数是hölder连续的，则相应的$α$ - fractal函数也是hölder连续的。此外，我们探讨了划分轴上$α$ - 属性功能的限制。此外，研究了多元$α$ - 属性功能及其限制的盒子尺寸和Hausdorff尺寸。在最后一节中，我们证明了分形功能的混合riemann-liouville分数积分满足自指的方程。
In this article, we construct the multivariate fractal interpolation functions for a given data points and explore the existence of $α$-fractal function corresponding to the multivariate continuous function defined on $[0,1]\times \cdots \times [0,1](q\text{-times})$. The parameters are selected such that the corresponding fractal version preserves some of the original function's properties, for instance, if the given function is Hölder continuous, then the corresponding $α$-fractal function is also Hölder continuous. Moreover, we explore the restriction of the $α$-fractal function on the co-ordinate axis. Furthermore, the box dimension and Hausdorff dimension of the graph of the multivariate $α$-fractal function and its restriction are investigated. In the last section, we prove that the mixed Riemann-Liouville fractional integral of fractal function satisfies a self-referential equation.
