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Abstract <p>In this work, we prove the Lyapunov-type inequality for a proposed boundary value problem with the generalized <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((k,\psi )\)</EquationSource> <!--ComMat2570195Selmani-m1--> </InlineEquation>-Hilfer proportional fractional operator. These results are more general. Afterwards, we give an application to eigenvalue problems and use that result to get an interval where the two-parameter Mittag-Leffler function has no zeros.</p>

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On Lyapunov-Type Inequality for a Fractional Boundary Value Problem with Generalized (k, ψ)-Hilfer Proportional Fractional Derivative and Applications

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • M. Selmani,
  • Ch. Harrat,
  • Y. Bouizem

摘要

Abstract

In this work, we prove the Lyapunov-type inequality for a proposed boundary value problem with the generalized \((k,\psi )\) -Hilfer proportional fractional operator. These results are more general. Afterwards, we give an application to eigenvalue problems and use that result to get an interval where the two-parameter Mittag-Leffler function has no zeros.