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

Author

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  • Sabiry, Abdelaziz
  • Kassidi, Abderrazak
  • Boulaaras, Salah
  • Guefaifia, Rafik

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.

Suggested Citation

  • Sabiry, Abdelaziz & Kassidi, Abderrazak & Boulaaras, Salah & Guefaifia, Rafik, 2026. "Nonlinear ψ-Hilfer fractional problem with measure data and two obstacle," Chaos, Solitons & Fractals, Elsevier, vol. 202(P2).
    • Handle: RePEc:eee:chsofr:v:202:y:2026:i:p2:s0960077925016376
    DOI: 10.1016/j.chaos.2025.117624
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    References listed on IDEAS

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    1. Kumar, Devendra & Singh, Jagdev & Baleanu, Dumitru & Sushila,, 2018. "Analysis of regularized long-wave equation associated with a new fractional operator with Mittag-Leffler type kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 155-167.
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