First and Second Fundamental Solutions of the Time-Fractional Telegraph Equation with Laplace or Dirac Operators

被引：12

作者：

Ferreira, M. ^{[1
,2
]}

Rodrigues, M. M. ^{[2
]}

Vieira, N. ^{[2
]}

机构：

[1] Polytech Inst Leiria, Sch Technol & Management, P-2411901 Leiria, Portugal

[2] Univ Aveiro, CIDMA Ctr Res & Dev Math & Applicat, Dept Math, Campus Univ Santiago, P-3810193 Aveiro, Portugal

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2018年 / 28卷 / 02期

关键词：

Time-fractional telegraph equation; Time-fractional telegraph Dirac operator; First and second fundamental solutions; Caputo fractional derivative; Multivariate Mittag-Leffler function; H-function of two variables; EIGENFUNCTIONS;

D O I：

10.1007/s00006-018-0858-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we obtain the first and second fundamental solutions (FS) of the multidimensional time-fractional equation with Laplace or Dirac operators, where the two time-fractional derivatives of orders alpha is an element of]0, 1] and beta is an element of]1, 2] are in the Caputo sense. We obtain representations of the FS in terms of Hankel transform, double Mellin-Barnes integrals, and H-functions of two variables. As an application, the FS are used to solve Cauchy problems of Laplace and Dirac type.

引用

页数：14

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