A modified Bessel-type integral transform and its compositions with fractional calculus operators on spaces Fp,μ and F′p,μ

被引：10

作者：

Glaeske, HJ

Kilbas, AA

Saigo, M ^{[1
]}

机构：

[1] Fukuoka Univ, Dept Appl Math, Fukuoka 8140180, Japan

[2] Univ Jena, Dept Math & Informat, D-07740 Jena, Germany

[3] Belarusian State Univ, Dept Math & Mech, Minsk 220050, BELARUS

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2000年 / 118卷 / 1-2期

关键词：

fractional calculus; McBride space; modified Bessel-type integral transform;

D O I：

10.1016/S0377-0427(00)00286-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper is devoted to study the integral transform (L(gamma,sigma)((beta))f)(x) = integral(0)(infinity)lambda(gamma sigma)((beta))(xt)f(t)dt (x>0)with the kernel lambda(gamma,sigma)((beta))(z)=beta/Gamma(gamma+1-1/beta)integral(1)(infinity)(t(beta)-1)(gamma-1/beta)t(sigma)e(-zt) dt for beta>0; Re(gamma)>1/beta-1; sigma element of R; Re(z)>0, which is a generalization of the modified Bessel function of the third kind of Macdonald function K-gamma(z). Properties of lambda(gamma,sigma)((beta))(z) investigated and compositions of the operator L-gamma,sigma((beta)) with the left- and right-sided Liouville fractional integrals and derivatives are proved. (C) 2000 Elsevier Science B.V. All rights reserved.

引用

页码：151 / 168

页数：18