Nonlinear ψ-Hilfer fractional problem with measure data and two obstacle

Abdelaziz Sabiry, Abderrazak Kassidi, Salah Boulaaras and Rafik Guefaifia

Chaos, Solitons & Fractals, 2026, vol. 202, issue P2

Abstract: This paper investigates a double-obstacle problem driven by a ψ-Hilfer fractional operator with variable exponent growth and a Hardy-type potential. In the setting of variable exponent Sobolev spaces, we prove existence and uniqueness of entropy solutions for Radon measure data absolutely continuous with respect to the p(⋅)-capacity, and establish nonexistence when the measure is supported on sets of zero capacity. The approach combines capacity estimates, measure decomposition, and variational techniques adapted to the ψ-Hilfer framework. These results generalize classical obstacle problem theory with measure data to a broader fractional and heterogeneous context, highlighting the interplay between variable exponents, Hardy singularities, and nonlocal effects.

Keywords: Capacity; Hardy-type; Singular potentials; Entropy solutions; Nonlinear equations (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:202:y:2026:i:p2:s0960077925016376

DOI: 10.1016/j.chaos.2025.117624

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