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… 

References

SHOWING 1-10 OF 44 REFERENCES
Introduction to Fourier analysis on Euclidean spaces (PMS-32)
Mathematical Methods for Physicists
Vector Analysis. Curved Coordinates, Tensors. Determinants and Matrices. Group Theory. Infinite Series. Functions of a Complex Variable I. Functions of a Complex Variable II. Differential Equations.
Sur une application de la derivée d’ordre non entier au calcul des probabilités
  • CR Acad. Sci
  • 1923
On the zeros of an integral function represented by Fourier’s integral
  • Messenger of Math. 1923;52:185–188
  • 1923
The fractional Clifford Fourier transform based on a deformed Hamiltonian for the harmonic oscillator
We derive a fractional Clifford-Fourier transform based on the deformations of the classical Hamiltonian for the harmonic oscillator. By the aid of the radial deformed Kelvin transforms we get a new
A Signed Measure on Path Space Related to Wiener Measure
On the eventual local positivity for polyharmonic heat equations
Fractional Riesz–Hilbert-Type Transforms and Associated Monogenic Signals
The fractional Hilbert transforms play a significant role in optics and signal processing because they interpolate between the near field and the far field. Mathematically, they interpolate between
An Introduction to Clifford Algebras and Spinors
...
...