A generalized contraction mapping applied for existence results for ordinary hybrid version of a generalized Sturm–Liouville–Langevin equations under $\Psi $-Hilfer fractional-order derivative

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2025年1月2日

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Hacen Serrai,
Brahim Tellab

摘要

This paper intends to study the existence of solutions for two ordinary hybrid versions of the generalized Sturm–Liouville–Langevin equation under different boundary conditions using a different approach that is based on the technique of $\alpha $ $α$ – $\varphi $ $φ$ -contraction via admissible mapping in the fixed point theorem. The $\Psi $ $Ψ$ -Hilfer fractional-order derivative is used to model these problems. To support and further illustrate our main findings, two examples are provided. The results are novel and extend some of the findings known in the literature.

A generalized contraction mapping applied for existence results for ordinary hybrid version of a generalized Sturm–Liouville–Langevin equations under \(\Psi \)-Hilfer fractional-order derivative

摘要