Ferreira, MiltonRodrigues, M. ManuelaVieira, Nelson2019-02-062019-02-062018-12-04M. Ferreira, M. M. Rodrigues, and N. Vieira, First and second fundamental solutions of the time-fractional telegraph equation of order 2α, AIP Conference Proceedings ICNPAA 2018 World Congress, 2046, 020079 (2018)http://hdl.handle.net/10400.8/3802In this work we obtain the first and second fundamental solutions of the multidimensional time-fractional equation of order 2α, α ∈]0, 1], where the two time-fractional derivatives are in the Caputo sense. We obtain representations of the fundamental solutions in terms of Hankel transform, double Mellin-Barnes integral, and H-functions of two variables. As an application, the fundamental solutions are used to solve a Cauchy problem and to study telegraph process with Brownian time.engTime-fractional equationTelegraph equationDirac operatorCaputo fractional derivativeH-functionsMultidimensional time-fractional equationMittag-Leffler functionsjournal article10.1063/1.5081599