论文标题
矢量值分形函数：分形尺寸和分数演算
Vector-valued fractal functions: Fractal dimension and Fractional calculus
论文作者
论文摘要
关于其图的实价分形插值功能和分形维的研究有许多研究。在本文中，我们的主要重点是研究矢量值分形插值函数及其Riemann-Liouville分数积分的维度结果。在这里，我们提供了一些结果，以确保矢量值函数的维度结果与实值函数完全不同。我们确定了矢量值分形插值函数的Hausdorff维度的有趣边界。我们还获得了在矢量值分形插值函数上支持的相关不变度度量的Hausdorff维度的边界。接下来，我们讨论了根据概率向量和收缩比的测量尺寸更有效的上限。此外，我们确定了矢量值分形插值函数的Riemann-Liouville分数积分图的一些维结果。
There are many research available on the study of real-valued fractal interpolation function and fractal dimension of its graph. In this paper, our main focus is to study the dimensional results for vector-valued fractal interpolation function and its Riemann-Liouville fractional integral. Here, we give some results which ensure that dimensional results for vector-valued functions are quite different from real-valued functions. We determine interesting bounds for the Hausdorff dimension of the graph of vector-valued fractal interpolation function. We also obtain bounds for the Hausdorff dimension of associated invariant measure supported on the graph of vector-valued fractal interpolation function. Next, We discuss more efficient upper bound for the Hausdorff dimension of measure in terms of probability vector and contraction ratios. Furthermore, we determine some dimensional results for the graph of the Riemann-Liouville fractional integral of a vector-valued fractal interpolation function.
