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math.AP2026
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…
math.AP2026
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…
math.AP2018
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.