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Journals / Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2021 / Cilt: 23 - Sayı: 2

Uniqueness theorems for some classes of nonlinear fractional differential equations in the Riemann-Liouville sense

Riemann-Liouville tip kesirli türevli lineer olmayan denklemlerin bazı sınıfları için teklik teoremleri

Müfit ŞAN
Pages
608–619
Publication Date
2021-07-04
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

These theorems improve the previously obtained results, and for their proofs pre-existing techniques are enriched by the tools of Lebesgue spaces.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, some classes of Riemann-Liouville fractional differential equations with right-hand side functions having a singularity with respect to their first variable and with a nonhomogeneous initial condition are considered.
📊
Key Findings & Data:First, it is briefly stated that under which conditions the existence of a local continuous solution of this initial value problem occurs.
💡
Conclusion & Impact:These theorems improve the previously obtained results, and for their proofs pre-existing techniques are enriched by the tools of Lebesgue spaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fractional differential equations · Riemann-Liouville derivative · existence and uniqueness

Abstract

In this study, some classes of Riemann-Liouville fractional differential equations with right-hand side functions having a singularity with respect to their first variable and with a nonhomogeneous initial condition are considered. First, it is briefly stated that under which conditions the existence of a local continuous solution of this initial value problem occurs. Later, uniqueness theorems were developed in types of Krasnosel’skii-Krein, Kooi, Roger and Banaś-Rivero, respectively. These theorems improve the previously obtained results, and for their proofs pre-existing techniques are enriched by the tools of Lebesgue spaces.

Özet

Bu çalışmada. sağ yan fonksiyonları birinci değişkenlerine göre singülerliğe sahip ve başlangıç koşulu homojen olmayan Riemann-Liouville kesirli diferansiyel denklemlerinin bazı sınıfları göz önüne alınmıştır. İlk önce, bu başlangıç-değer probleminin bir lokal sürekli çözümünün varlığını hangi koşular altında gerçekleştiği kısaca ifade edilmiştir. Daha sonra ise, sırasıyla Krasnosel’skii-Krein, Kooi, Roger ve Banaś-Rivero tiplerinde teklik teoremleri ortaya çıkarılmıştır. Bu teoremler daha önceden elde edilen sonuçları geliştirken, bu teoremlerin ispatları için, daha önceden var olan teknikler Lebesgue uzaylarının araçları ile zenginleştirilmiştir.

🔖

Cite This Article

ŞAN, M. (2021). Uniqueness theorems for some classes of nonlinear fractional differential equations in the Riemann-Liouville sense. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 23 - Sayı: 2, 608–619. https://ajindex.com/articles/250743

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