• DOI:10.1002/mma.7714
• Corpus ID: 233024690

On fundamental solutions of higher‐order space‐fractional Dirac equations

@article{Faustino2021OnFS,
  title={On fundamental solutions of higher‐order space‐fractional Dirac equations},
  author={N. Faustino},
  journal={Mathematical Methods in the Applied Sciences},
  year={2021}
}

• N. Faustino
• Published 3 April 2021
• Mathematics
• Mathematical Methods in the Applied Sciences

involving the fractional Laplacian −(−Δ) 2 of order , with 2m ≤ < 2m + 2 (m ∈ N), and the exponentiation operator exp ( i 2  as the hypercomplex counterpart of the fractional Riesz-Hilbert transform carrying the skewness parameter , with values in the range | | ≤ min{ − 2m, 2m+ 2 − }. Such model problem permits us to obtain hypercomplex counterparts for the fundamental solutions of higher-order heat-type equations )tFM (x, t) = M ()x) FM (x, t) (M = 2, 3,...) in case where the even powers resp. odd powers D2m = (−Δ) (M = = 2m) resp. D2m+1 = (−Δ) 1 2 (M = = 2m + 1) of D are being considered.