On some operators involving Hadamard derivatives

被引：63

作者：

Garra, Roberto ^{[1
]}

Polito, Federico ^{[2
]}

机构：

[1] Sapienza Univ Roma, Dipartimento Sci Base & Appl Ingn, I-00161 Rome, Italy

[2] Univ Turin, Dipartimento Matemat, I-10123 Turin, Italy

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2013年 / 24卷 / 10期

关键词：

Hadamard derivatives; alpha-Mittag-Leffler functions; alpha L-exponential functions; Lamb-Bateman equation; hyper-Bessel operators;

D O I：

10.1080/10652469.2012.756875

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce a novel Mittag-Leffler-type function and study its properties in relation to some integro-differential operators involving Hadamard fractional derivatives or hyper-Bessel-type operators. We discuss then the utility of these results to solve some integro-differential equations involving these operators by means of operational methods. We show the advantage of our approach through some examples. Among these, an application to a modified Lamb-Bateman integral equation is presented.

引用

页码：773 / 782

页数：10

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