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.
First and second fundamental solutions of the time-fractional telegraph equation of order 2α
ICNPAA 2018 WORLD CONGRESS: 12th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences ; 2018 ; Yerevan, Armenia
AIP Conference Proceedings ; 2046 , 1
04.12.2018
9 pages
Aufsatz (Konferenz)
Elektronische Ressource
Englisch
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