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.
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页码：441 / 462
页数：22
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