Convolutional Approach to Fractional Calculus for Distributions of Several Variables

被引：0
|
作者：
Svetlana Mincheva-Kaminska
机构：
[1] University of Rzeszów,Faculty of Mathematics and Natural Sciences
来源：
Fractional Calculus and Applied Analysis | 2016年 / 19卷
关键词：
Primary 26A33; Secondary 46F10; 46F05; convolution of distributions; partial fractional derivatives of distributions; fractional partial differential equations;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We extend the semigroup {Φλ}λ∈ℂ of Gel’fand and Shilov to the semigroup {Φλ}λ∈ℂn and the one-dimensional fractional calculus of distributions to the case of distributions on ℝn with supports in the nonnegative cone ℝ̄n+. We use distributional mixed derivatives of an arbitrary complex order to solve Abel’s multidimensional integral equation and a distributional fractional differential equation of wave type.
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页码：441 / 462
页数：21
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