On a connection between the \(N\)-dimensional fractional Laplacian and 1-D operators on lattices

DOI10.1016/j.jmaa.2022.126051zbMath1489.39027OpenAlexW4210655409MaRDI QIDQ2669357

Marina Murillo-Arcila, Carlos Lizama

Publication date: 9 March 2022

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2022.126051

zbMATH Keywords

\(N\)-dimensional discrete fractional Laplaciansemidiscrete heat semigroup

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Discrete version of topics in analysis (39A12) Difference operators (39A70)

Related Items (2)

Time-step heat problem on the mesh: asymptotic behavior and decay rates ⋮ Well-posedness for fractional Cauchy problems involving discrete convolution operators

Cites Work

• Unnamed Item
• On a connection between the discrete fractional Laplacian and superdiffusion
• Lattice fractional calculus
• Explicit solutions to dynamic diffusion-type equations and their time integrals
• On a connection between powers of operators and fractional Cauchy problems
• Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications
• Hölder-Lebesgue regularity and almost periodicity for semidiscrete equations with a fractional Laplacian
• Generalized Cesàro operators, fractional finite differences and gamma functions
• Brownian-time processes: The PDE connection and the half-derivative generator
• Large time behaviour for the heat equation on \(\mathbb{Z} \), moments and decay rates
• Asymptotic behavior of solutions to the semidiscrete diffusion equation
• A transference principle for nonlocal operators using a convolutional approach: fractional monotonicity and convexity
• Exact discretization of fractional Laplacian
• Path Laplacian operators and superdiffusive processes on graphs. I: One-dimensional case
• Harmonic analysis associated with a discrete Laplacian
• Well-posedness and maximum principles for lattice reaction-diffusion equations
• Almost automorphic mild solutions to fractional partial difference-differential equations
• Fractional Central Differences and Derivatives
• Brownian subordinators and fractional Cauchy problems
• Two‐sided and regularised Riesz‐Feller derivatives
• Anomalous diffusion in one-dimensional disordered systems: a discrete fractional Laplacian method
• Fundamental solutions for discrete dynamical systems involving the fractional Laplacian
• Discrete Bessel functions and partial difference equations
• The Poisson distribution, abstract fractional difference equations, and stability
• Waves with Power-Law Attenuation
• Lattice Dynamical Systems Associated with a Fractional Laplacian

This page was built for publication: On a connection between the \(N\)-dimensional fractional Laplacian and 1-D operators on lattices