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<p>In this article, we propose and study a novel class of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\varPhi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>Φ</mi> </math></EquationSource> </InlineEquation>-Hilfer proportional fractional hybrid Langevin equations subject to nonlocal boundary conditions. We examine the existence and uniqueness of solutions using Dhage’s fixed point theorem and the contraction mapping principle. Furthermore, we investigate the stability aspects of the proposed system, including Ulam-Hyers stability and its generalized form under suitable assumptions. A numerical example is provided to illustrate the theoretical findings and to show the practical significance of our results.</p>

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ON EXISTENCE AND STABILITY OF SOLUTIONS FOR \(\varPhi \)-HILFER PROPORTIONAL FRACTIONAL HYBRID LANGEVIN PROBLEMS WITH NONLOCAL BOUNDARY CONDITIONS

  • 期刊论文

  • 发表日期：

    2026年1月28日

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  • Mohamed El Fadouaki,
  • Hamid Lmou,
  • Khalid Hilal,
  • Ahmed Kajouni

摘要

In this article, we propose and study a novel class of \(\varPhi \) Φ -Hilfer proportional fractional hybrid Langevin equations subject to nonlocal boundary conditions. We examine the existence and uniqueness of solutions using Dhage’s fixed point theorem and the contraction mapping principle. Furthermore, we investigate the stability aspects of the proposed system, including Ulam-Hyers stability and its generalized form under suitable assumptions. A numerical example is provided to illustrate the theoretical findings and to show the practical significance of our results.