First and second fundamental solutions of the time-fractional telegraph equation with Laplace or Dirac operators

Ferreira, Milton; Rodrigues, Manuela M.; Vieira, Nelson

http://hdl.handle.net/10400.8/3257

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Authors

Ferreira, Milton

Rodrigues, Manuela M.

Vieira, Nelson

Abstract(s)

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 α ∈]0, 1] and β ∈]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.

Description

Acknowledgement: The authors were supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT–Funda¸cˆao para a Ciˆencia e a Tecnologia”), within project UID/MAT/ 0416/2013. N. Vieira is Auxiliar Researcher, under the FCT Researcher Program 2014 (Ref: IF/00271/2014).

Keywords

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

URI

http://hdl.handle.net/10400.8/3257

Citation

Ferreira M., Rodrigues M.M., and Vieira N. (2018). First and second fundamental solutions of the time-fractional telegraph equation with Laplace or Dirac operators, Adv. Appl. Clifford Algebras, 28(2), Article No.42 - pp. 1-14.