Ferreira, MiltonRodrigues, Manuela M.Vieira, Nelson2018-05-282019-05-152018-05Ferreira 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. 1-14.0188-7009http://hdl.handle.net/10400.8/3257Acknowledgement: 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).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.engTime-fractional telegraph equationTime-fractional telegraph Dirac operatorFirst and second fundamental solutionsCaputo fractional derivativeMultivariate Mittag-Leffler functionH-function of two variablesjournal articleDOI 10.1007/s00006-018-0858-7