SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Research

Fractional exponential operators and time-fractional telegraph equation

Alireza Ansari

Author Affiliations

Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran

Boundary Value Problems 2012, 2012:125  doi:10.1186/1687-2770-2012-125

Published: 29 October 2012

Abstract

In this paper, the Bromwich integral for the inverse Mellin transform is used for finding an integral representation for a fractional exponential operator. This operator can be considered as an approach for solving partial fractional differential equations. Also, application of this operator for obtaining a formal solution of the time-fractional telegraph equation is discussed.

MSC: 26A33, 35A22, 44A10.

Keywords:
Laplace transform; Mellin transform; partial fractional differential equation; Wright function