What is the fractional Laplacian? A comparative review with new results
The fractional Laplacian in R d, which we write as (− Δ) α/2 with α∈(0, 2), has multiple
equivalent characterizations. Moreover, in bounded domains, boundary conditions must be …
equivalent characterizations. Moreover, in bounded domains, boundary conditions must be …
A review of applications of fractional calculus in Earth system dynamics
Fractional calculus has been used to model various hydrologic processes for 15 years. Yet,
there are still major gaps between real-world hydrologic dynamics and fractional-order …
there are still major gaps between real-world hydrologic dynamics and fractional-order …
[LIVRE][B] Handbook of peridynamic modeling
This handbook covers the peridynamic modeling of failure and damage. Peridynamics is a
reformulation of continuum mechanics based on integration of interactions rather than …
reformulation of continuum mechanics based on integration of interactions rather than …
nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications
Physics-informed neural networks (PINNs) are effective in solving inverse problems based
on differential and integro-differential equations with sparse, noisy, unstructured, and multi …
on differential and integro-differential equations with sparse, noisy, unstructured, and multi …
A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations
In this paper, a fast linearized conservative finite element method is studied for solving the
strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme …
strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme …
Data-driven learning of nonlocal physics from high-fidelity synthetic data
A key challenge to nonlocal models is the analytical complexity of deriving them from first
principles, and frequently their use is justified a posteriori. In this work we extract nonlocal …
principles, and frequently their use is justified a posteriori. In this work we extract nonlocal …
Fractional modeling in action: A survey of nonlocal models for subsurface transport, turbulent flows, and anomalous materials
Modeling of phenomena such as anomalous transport via fractional-order differential
equations has been established as an effective alternative to partial differential equations …
equations has been established as an effective alternative to partial differential equations …
What is the fractional Laplacian?
The fractional Laplacian in R^ d has multiple equivalent characterizations. Moreover, in
bounded domains, boundary conditions must be incorporated in these characterizations in …
bounded domains, boundary conditions must be incorporated in these characterizations in …
[HTML][HTML] Reprint of: Boundary conditions for fractional diffusion
This paper derives physically meaningful boundary conditions for fractional diffusion
equations, using a mass balance approach. Numerical solutions are presented, and …
equations, using a mass balance approach. Numerical solutions are presented, and …
[LIVRE][B] Nonlocal Modeling, Analysis, and Computation: Nonlocal Modeling, Analysis, and Computation
Q Du - 2019 - SIAM
Nonlocal Modeling, Analysis, and Computation : Back Matter Page 1 Bibliography [1] L.
ABDELOUHAB, J. BONA, M. FELLAND, AND J.-C. SAUT, Nonlocal models for nonlinear …
ABDELOUHAB, J. BONA, M. FELLAND, AND J.-C. SAUT, Nonlocal models for nonlinear …