Fractional operators applied to geophysical electromagnetics
CJ Weiss, BG van Bloemen Waanders… - Geophysical Journal …, 2020 - academic.oup.com
SUMMARY A growing body of applied mathematics literature in recent years has focused on
the application of fractional calculus to problems of anomalous transport. In these analyses …
the application of fractional calculus to problems of anomalous transport. In these analyses …
Spectral approximation of fractional PDEs in image processing and phase field modeling
Fractional differential operators provide an attractive mathematical tool to model effects with
limited regularity properties. Particular examples are image processing and phase field …
limited regularity properties. Particular examples are image processing and phase field …
Fractional operators with inhomogeneous boundary conditions: Analysis, control, and discretization
H Antil, J Pfefferer, S Rogovs - arXiv preprint arXiv:1703.05256, 2017 - arxiv.org
In this paper we introduce new characterizations of spectral fractional Laplacian to
incorporate nonhomogeneous Dirichlet and Neumann boundary conditions. The classical …
incorporate nonhomogeneous Dirichlet and Neumann boundary conditions. The classical …
Compactness results for a Dirichlet energy of nonlocal gradient with applications
We prove two compactness results for function spaces with finite Dirichlet energy of half‐
space nonlocal gradients. In each of these results, we provide sufficient conditions on a …
space nonlocal gradients. In each of these results, we provide sufficient conditions on a …
Optimal control of fractional semilinear PDEs
In this paper, we consider the optimal control of semilinear fractional PDEs with both spectral
and integral fractional diffusion operators of order 2s with s∈(0, 1). We first prove the …
and integral fractional diffusion operators of order 2s with s∈(0, 1). We first prove the …
A Gevrey class semigroup for a thermoelastic plate model with a fractional Laplacian: Between the Euler-Bernoulli and Kirchhoff models.
In a bounded domain, we consider a thermoelastic plate with rotational forces. The rotational
forces involve the spectral fractional Laplacian, with power parameter 0≤ θ≤ 1. The model …
forces involve the spectral fractional Laplacian, with power parameter 0≤ θ≤ 1. The model …
Regularity and stability for a plate model involving fractional rotational forces and damping
L Tebou - Zeitschrift für angewandte Mathematik und Physik, 2021 - Springer
We consider a damped plate model with rotational forces in a bounded domain. The plate is
either clamped or hinged. The rotational forces and damping involve the spectral fractional …
either clamped or hinged. The rotational forces and damping involve the spectral fractional …
[PDF][PDF] Optimal control of the coefficient for the regional fractional p-Laplace equation: approximation and convergence
In this paper we study optimal control problems with the regional fractional p-Laplace
equation, of order s∈(0, 1) and p∈[2,∞), as constraints over a bounded open set with …
equation, of order s∈(0, 1) and p∈[2,∞), as constraints over a bounded open set with …
External optimal control of fractional parabolic PDEs
In [Antil et al. Inverse Probl. 35 (2019) 084003.] we introduced a new notion of optimal
control and source identification (inverse) problems where we allow the control/source to be …
control and source identification (inverse) problems where we allow the control/source to be …
Optimal control of fractional elliptic PDEs with state constraints and characterization of the dual of fractional-order Sobolev spaces
This paper introduces the notion of state constraints for optimal control problems governed
by fractional elliptic partial differential equations. Several mathematical tools are developed …
by fractional elliptic partial differential equations. Several mathematical tools are developed …