Ψ-Bielecki-type norm inequalities for a generalized Sturm-Liouville-Langevin differential equation involving Ψ-Caputo fractional derivative

被引：10

作者：

Serrai, Hacen ^{[1
]}

Tellab, Brahim ^{[1
]}

Etemad, Sina ^{[2
]}

Avci, Ibrahim ^{[3
]}

Rezapour, Shahram ^{[2
,4
,5
]}

机构：

[1] Kasdi Merbah Univ, Lab Appl Math, Ouargla, Algeria

[2] Azarbaijan Shahid Madani Univ, Dept Math, Tabriz, Iran

[3] Final Int Univ, Fac Engn, Dept Comp Engn, Via Mersin 10, Kyrenia, Northern Cyprus, Turkiye

[4] Insurance Res Ctr, Tehran, Iran

[5] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung, Taiwan

来源：

BOUNDARY VALUE PROBLEMS | 2024年 / 2024卷 / 01期

关键词：

Psi-Caputo derivative; Psi-Bielecki-type norm; Fractional Sturm-Liouville equation; Fractional Langevin equation; Fixed point theorems; Generalized Gronwall inequality; Ulam stability; RESPECT;

D O I：

10.1186/s13661-024-01863-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The present research work investigates some new results for a fractional generalized Sturm-Liouville-Langevin (FGSLL) equation involving the Psi-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 Psi-Bielecki-type. Meanwhile, the fixed-point theorems of the Leray-Schauder and Krasnoselskii type associated with the Psi-Bielecki-type norm are used to derive the existence properties by removing some strong conditions. We use the generalized Gronwall-type inequality to discuss Ulam-Hyers (UH), generalized Ulam-Hyers (GUH), Ulam-Hyers-Rassias (UHR), and generalized Ulam-Hyers-Rassias (GUHR) stability of these solutions. Lastly, three examples are provided to show the effectiveness of our main results for different cases of (FGSLL)-problem such as Caputo-type Sturm-Liouville, Caputo-type Langevin, Caputo-Erdelyi-Kober-type Langevin problems.

引用

页数：45

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