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

  title={On fundamental solutions of higher‐order space‐fractional Dirac equations},
  author={N. Faustino},
  journal={Mathematical Methods in the Applied Sciences},
  • 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… 


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