CONVOLUTIONAL APPROACH TO FRACTIONAL CALCULUS FOR DISTRIBUTIONS OF SEVERAL VARIABLES

被引：2

作者：

Mincheva-Kaminska, Svetlana ^{[1
]}

机构：

[1] Univ Rzeszow, Fac Math & Nat Sci, Prof Pigonia 1, PL-35310 Rzeszow, Poland

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2016年 / 19卷 / 02期

关键词：

convolution of distributions; partial fractional derivatives of distributions; fractional partial differential equations; DERIVATIVES; TRANSFORM;

D O I：

10.1515/fca-2016-0023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We extend the semigroup {phi(lambda)}(lambda is an element of C) of Gel'fand and Shilov to the semigroup {phi(lambda)}(lambda is an element of Cn) and the one-dimensional fractional calculus of distributions to the case of distributions on R-n with supports in the nonnegative cone (R) over bar (n)(+). 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.

引用

页码：441 / 462

页数：22

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