6 papers
The upper semi-Fredholm radius, extensions of restrictions, and subprojectivity
Abdelhalim Azzouz
For a bounded operator between Banach spaces, let be its distance to the operators that are not upper semi-Fredholm, and let $\inn(T)$ be Schechter's quantity $\inf\|T…
A Gaussian-based spatially weighted loss formulation for Physics-Informed Neural Networks with Shocks
Kheir-eddine Otmani, Abdelhalim Azzouz, Nourelhouda Groun +1
Physics-informed neural networks (PINNs) often struggle to resolve shocks because smooth neural representations and globally averaged residual losses tend to underemphasize localiz…
A nonlocal transmission problem on a hybrid continuous-discrete domain
Hafida Abbas, Abdelhalim Azzouz
We study a quadratic nonlocal variational problem on a hybrid domain formed by a compact interval and finitely many discrete points. The associated energy splits into continuous, d…
Fractional Sobolev Spaces and Variational Problems with Variable-Order Operators on Time Scales
Hafida Abbas, Abdelhalim Azzouz
We construct fractional Sobolev spaces on arbitrary time scales, both in one dimension and on product time scales. In 1D, we define throu…
Towards a Gagliardo-Type Theory of Fractional Sobolev Spaces on Arbitrary Time Scales
Hafida Abbas, Abdelhalim Azzouz, Praveen Agarwal +1
We propose a systematic Gagliardo-type formulation of fractional Sobolev spaces on arbitrary time scales, based on the Lebesgue Delta-measure and the off-diagonal interaction domai…
Fractional Kirchhoff problem with Hardy potentiel: Breaking of resonance
Boumediene Abdellaoui, Abdelhalim Azzouz, Ahmed Bensedik
The present work is concerned with existence of positive solutions for a class of fractional equation involving a Kirchhoff term and singular potential.