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Peer-reviewedCC BYOpen Mathematics

Ulam–Hyers stability for hybrid differential equations with mixed fractional derivatives and the μ-Laplacian operator

  • Maazouz Kadda1
  • Ouardani Abderrahmane1
  • Bechayeb Rabah1
  • Moumen Abdelkader2
  • Bouye Mohamed3
  1. 1Department of Mathematics, Faculty of Mathematics and Computer Science, Ibn Khaldoun University of Tiaret, Tiaret, 14000, Algeria
  2. 2Department of Mathematics, College of Science, University of Hail, Ha’il55473, Saudi Arabia
  3. 3Department of Mathematics, Faculty of Sciences, King Khalid University, PO Box 9004, Abha, Saudi Arabia
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Abstract

In this work, we investigate the Ulam–Hyers stability and generalized Ulam–Hyers stability for a class of hybrid differential equations involving both proportional fractional derivatives and classical derivatives, coupled with the μ-Laplacian operator and subject to fractional integral boundary conditions. Building upon recent existence results for this class of equations, we establish sufficient conditions under which solutions exhibit Ulam–Hyers stability. The analysis relies on nonlinear analysis techniques and properties of the μ-Laplacian operator. Two illustrative examples are provided: one for classical Ulam–Hyers stability and another for uniform stability under a variable perturbation described by a power-type control function.

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Cite

BibTeXRIS
BibTeX
@article{kadda2026ulamhyers,
  title = {{Ulam–Hyers stability for hybrid differential equations with mixed fractional derivatives and the μ-Laplacian operator}},
  author = {Maazouz Kadda and Ouardani Abderrahmane and Bechayeb Rabah and Moumen Abdelkader and Bouye Mohamed},
  journal = {Open Mathematics},
  year = {2026},
  month = oct,
  doi = {10.1515/math-2025-0296},
  url = {https://doi.org/10.1515/math-2025-0296},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Ulam–Hyers stability for hybrid differential equations with mixed fractional derivatives and the μ-Laplacian operator
AU  - Maazouz Kadda
AU  - Ouardani Abderrahmane
AU  - Bechayeb Rabah
AU  - Moumen Abdelkader
AU  - Bouye Mohamed
PY  - 2026
DA  - 2026/10/26
JO  - Open Mathematics
DO  - 10.1515/math-2025-0296
UR  - https://doi.org/10.1515/math-2025-0296
AB  - In this work, we investigate the Ulam–Hyers stability and generalized Ulam–Hyers stability for a class of hybrid differential equations involving both proportional fractional derivatives and classical derivatives, coupled with the μ-Laplacian operator and subject to fractional integral boundary conditions. Building upon recent existence results for this class of equations, we establish sufficient conditions under which solutions exhibit Ulam–Hyers stability. The analysis relies on nonlinear analysis techniques and properties of the μ-Laplacian operator. Two illustrative examples are provided: one for classical Ulam–Hyers stability and another for uniform stability under a variable perturbation described by a power-type control function.
SN  - 2391-5455
ER  -