二元分形插值曲面的微积分
The Calculus Of Bivariate Fractal Interpolation Surfaces
摘要：
本文研究了二元分形插值函数的偏积分和偏导数。证明了二元分形插值函数的混合Riemann-Liouville分数次积分和导数的$γ= (p, q); p > 0,q > 0$阶也是对应于迭代函数系（IFS）的二元插值函数.进一步讨论了二元分形插值函数的积分变换和分数阶积分变换。
英文摘要：
In this article, we investigate partial integrals and partial derivatives of bivariate fractal interpolation functions. We prove also that the mixed Riemann-Liouville fractional integral and derivative of order $γ= (p, q); p > 0,q > 0$, of bivariate fractal interpolation functions are again bivariate interpolation functions corresponding to some iterated function system (IFS). Furthermore, we discuss the integral transforms and fractional order integral transforms of the bivariate fractal interpolation functions.
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