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<p>This article investigates the solvability of a class of nonlinear fractional boundary value problems involving the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation>-Caputo fractional derivative of order <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\alpha &gt; n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>&gt;</mo> <mi>n</mi> </mrow> </math></EquationSource> </InlineEquation>. Using the Banach contraction principle and Krasnoselskii’s fixed point theorem, we establish new existence and uniqueness results under standard Lipschitz and boundedness conditions. The general form of the boundary conditions allows the incorporation of several existing models as special cases. Illustrative examples are provided to demonstrate the applicability and effectiveness of the theoretical findings.</p>

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Existence results for nonlinear boundary value problems involving generalized \(\psi \)-Caputo fractional derivatives

  • 期刊论文

  • 发表日期：

    2025年10月15日

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  • Salma Solhi,
  • Ahmed Kajouni,
  • Khalid Hilal

摘要

This article investigates the solvability of a class of nonlinear fractional boundary value problems involving the \(\psi \) ψ -Caputo fractional derivative of order \(\alpha > n\) α > n . Using the Banach contraction principle and Krasnoselskii’s fixed point theorem, we establish new existence and uniqueness results under standard Lipschitz and boundedness conditions. The general form of the boundary conditions allows the incorporation of several existing models as special cases. Illustrative examples are provided to demonstrate the applicability and effectiveness of the theoretical findings.