First and second fundamental solutions of the time-fractional telegraph equation of order 2α

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

http://hdl.handle.net/10400.8/3802

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Authors

Ferreira, Milton

Rodrigues, M. Manuela

Vieira, Nelson

Abstract(s)

In 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.

Keywords

Time-fractional equation Telegraph equation Dirac operator Caputo fractional derivative H-functions Multidimensional time-fractional equation Mittag-Leffler functions

URI

http://hdl.handle.net/10400.8/3802

Citation

M. 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)