论文标题
Riemann-Liouville衍生品在可集成分布的空间上
Riemann-Liouville derivative over the space of integrable distributions
论文作者
论文摘要
在本文中，我们将Riemann-Liouville差异和积分运算符概括为Henstock-Kurzweil Antegrable分布的空间，$ d_ {hk} $。我们获得了分数衍生物和积分的新基本属性，这是分数微积分的基本定理的一般版本，Riemann-Liouville积分运算符的Semigroup属性以及Riemann-Liouville积分和差异操作员之间的关系。同样，我们实现了ABEL积分方程的解决方案的广义表征。最后，我们展示了分数衍生物和积分的傅立叶变换的关系。这些结果基于分布Henstock-Kurzweil积分和卷积的特性。
In this paper, we generalize the Riemann-Liouville differential and integral operators on the space of Henstock-Kurzweil integrable distributions, $D_{HK}$. We obtain new fundamental properties of the fractional derivative and integral, a general version of the fundamental theorem of fractional calculus, semigroup property for the Riemann-Liouville integral operators and relations between the Riemann-Liouville integral and differential operators. Also, we achieve a generalized characterization of the solution for the Abel integral equation. Finally, we show relations for the Fourier transform of fractional derivative and integral. These results are based on the properties of the distributional Henstock-Kurzweil integral and convolution.
