# On fractional semidiscrete Dirac operators of L\'evy-Leblond type

@inproceedings{Faustino2021OnFS, title={On fractional semidiscrete Dirac operators of L\'evy-Leblond type}, author={N. Faustino}, year={2021} }

In this paper we introduce a wide class of space-fractional and time-fractional semidiscrete Dirac operators of L´evy-Leblond type on the semidiscrete space-time lattice h Z n × [0 , ∞ ) ( h > 0), resembling to fractional semidiscrete counterparts of the so-called parabolic Dirac operators. The methods adopted here are fairly operational, relying mostly on the algebraic manipulations involving Clif-ford algebras, discrete Fourier analysis techniques as well as standard properties of the…

## References

SHOWING 1-10 OF 48 REFERENCES

### A Fractional Dirac Operator

- Mathematics
- 2016

Based on the Riesz potential, S. Samko and coworkers studied the fractional integro-differentiation of functions of many variables which is a fractional power of the Laplace operator. We will extend…

### Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators

- Mathematics
- 2017

### Fundamental solutions for semidiscrete evolution equations via Banach algebras

- MathematicsAdvances in difference equations
- 2021

The linear and algebraic structures and their norms and spectra in the Lebesgue space of summable sequences are presented and the fractional powers of these generators are identified and the subordination principle is applied.

### The fundamental solution of the space-time fractional diffusion equation

- Mathematics
- 2007

We deal with the Cauchy problem for the space-time fractional diffusion equation, which is obtained from the standard diffusion equation by replacing the second-order space derivative with a…

### Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications

- Mathematics
- 2016

### Z2*Z2-graded Lie symmetries of the Levy-Leblond equations

- Mathematics
- 2016

This paper exhaustively investigates the symmetries of the $(1+1)$-dimensional L\'evy-Leblond Equations, both in the free case and for the harmonic potential, and introduces a new feature, explaining the existence of first-order differential symmetry operators not entering the super Schr\"odinger algebra.

### A note on the discrete Cauchy‐Kovalevskaya extension

- MathematicsMathematical Methods in the Applied Sciences
- 2018

In this paper, we exploit the umbral calculus framework to reformulate the so‐called discrete Cauchy‐Kovalevskaya extension in the scope of hypercomplex variables. The key idea is to consider not…

### A conformal group approach to the Dirac–Kähler system on the lattice

- Mathematics
- 2016

Starting from the representation of the (n − 1) + n − dimensional Lorentz pseudo-sphere on the projective space PRn,n, we propose a method to derive a class of solutions underlying to a Dirac–Kahler…