论文标题
二维分数正交衍生物
The two-dimensional fractional orthogonal derivative
论文作者
论文摘要
本文是作者论文中第6章的编辑和缩短版本。首先，一维正交导数将扩展到二维情况。在二维情况下，我们必须定义整合区域。在本文中，我们处理正方形区域和三角形区域上的整合，在最后一个情况下，我们使用以appell函数表示的生物表决性多项式。接下来，二维正交衍生物将扩展到二维分数正交衍生物。结果高度取决于$ f_1 $，\ $ f_2 $和$ f_3 $ appell功能。
This paper is an edited and shortened version of Chapter 6 from the thesis of the author. First the one dimensional orthogonal derivative will be extended to the two-dimensional case. In the two-dimensional case we have to define the region of integration. In this paper we treat the integration over the square region and over the triangle region where in the last case we use biorthogonal polynomials expressed in terms of Appell functions. Next the two-dimensional orthogonal derivative will be extended to the two-dimensional fractional orthogonal derivative. The results are highly dependent on the $F_1$,\ $F_2$ and $F_3$ Appell functions.
