2024
DOI: 10.1186/s13661-024-01863-1
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Ψ-Bielecki-type norm inequalities for a generalized Sturm–Liouville–Langevin differential equation involving Ψ-Caputo fractional derivative

Hacen Serrai,
Brahim Tellab,
Sina Etemad
et al.

Abstract: The present research work investigates some new results for a fractional generalized Sturm–Liouville–Langevin (FGSLL) equation involving the Ψ-Caputo fractional derivative with a modified argument. We prove the uniqueness of the solution using the Banach contraction principle endowed with a norm of the Ψ-Bielecki-type. Meanwhile, the fixed-point theorems of the Leray–Schauder and Krasnoselskii type associated with the Ψ-Bielecki-type norm are used to derive the existence properties by removing some strong cond… Show more

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