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 …

Spectral approximation of fractional PDEs in image processing and phase field modeling

H Antil, S Bartels - Computational Methods in Applied Mathematics, 2017 - degruyter.com
Fractional differential operators provide an attractive mathematical tool to model effects with
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 …

Compactness results for a Dirichlet energy of nonlocal gradient with applications

Z Han, T Mengesha, X Tian - Numerical Methods for Partial …, 2024 - Wiley Online Library
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 …

Optimal control of fractional semilinear PDEs

H Antil, M Warma - ESAIM: Control, Optimisation and Calculus of …, 2020 - esaim-cocv.org
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 …

A Gevrey class semigroup for a thermoelastic plate model with a fractional Laplacian: Between the Euler-Bernoulli and Kirchhoff models.

V Keyantuo, L Tebou, M Warma - Discrete & Continuous …, 2020 - search.ebscohost.com
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 …

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 …

[PDF][PDF] Optimal control of the coefficient for the regional fractional p-Laplace equation: approximation and convergence

H Antil, M Warma - Math. Control Relat. Fields, 2019 - researchgate.net
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 …

External optimal control of fractional parabolic PDEs

H Antil, D Verma, M Warma - ESAIM: Control, Optimisation and …, 2020 - esaim-cocv.org
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 …

Optimal control of fractional elliptic PDEs with state constraints and characterization of the dual of fractional-order Sobolev spaces

H Antil, D Verma, M Warma - Journal of optimization theory and …, 2020 - Springer
This paper introduces the notion of state constraints for optimal control problems governed
by fractional elliptic partial differential equations. Several mathematical tools are developed …