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Fundamental solution of the time‐fractional telegraph Dirac operator
Author(s) -
Ferreira M.,
Rodrigues M. M.,
Vieira N.
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4511
Subject(s) - mathematics , operator (biology) , dirac operator , cauchy distribution , fractional calculus , dimension (graph theory) , dirac (video compression format) , mittag leffler function , representation (politics) , mathematical analysis , series (stratigraphy) , initial value problem , mathematical physics , pure mathematics , quantum mechanics , law , paleontology , biochemistry , chemistry , physics , repressor , politics , biology , political science , transcription factor , neutrino , gene
Summary In this work, we obtain the fundamental solution (FS) of the multidimensional time‐fractional telegraph Dirac operator where the 2 time‐fractional derivatives of orders α ∈]0,1] and β ∈]1,2] are in the Caputo sense. Explicit integral and series representation of the FS are obtained for any dimension. We present and discuss some plots of the FS for some particular values of the dimension and of the fractional parameters α and β . Finally, using the FS, we study some Poisson and Cauchy problems.