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Journals / Sigma Mühendislik ve Fen Bilimleri Dergisi / 2019 / Cilt: 37 - Sayı: 4

THE EXISTENCE OF POSITIVE SOLUTIONS AND A LYAPUNOV TYPE INEQUALITY FOR BOUNDARY VALUE PROBLEMS OF THE FRACTIONAL CAPUTO-FABRIZIO DIFFERENTIAL EQUATIONS

Şuayip TOPRAKSEVEN
Pages
1129–1137
Publication Date
2019-12-01
DOI
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AI Summary & Key Takeaways

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

Finally, we gave some numerical examples to validate the theoretical findings.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, a Lyapunov-type inequality and the existence of the positive solutions for boundary value problems of the nonlinear fractional Caputo-Fabrizio differential equation have been presented.
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Key Findings & Data:By using the Guo Krasnoselskii’s fixed point theorem on cone and the properties of the associated Green`s function, we prove the existence of the positive solution.
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Conclusion & Impact:Finally, we gave some numerical examples to validate the theoretical findings.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Lyapunov-type inequality · fractional Caputo-Fabrizio derivative · Green’s function

Abstract

In this paper, a Lyapunov-type inequality and the existence of the positive solutions for boundary value problems of the nonlinear fractional Caputo-Fabrizio differential equation have been presented. By using the Guo Krasnoselskii’s fixed point theorem on cone and the properties of the associated Green`s function, we prove the existence of the positive solution. Finally, we gave some numerical examples to validate the theoretical findings.

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Cite This Article

TOPRAKSEVEN, Ş. (2019). THE EXISTENCE OF POSITIVE SOLUTIONS AND A LYAPUNOV TYPE INEQUALITY FOR BOUNDARY VALUE PROBLEMS OF THE FRACTIONAL CAPUTO-FABRIZIO DIFFERENTIAL EQUATIONS. Sigma Mühendislik ve Fen Bilimleri Dergisi, Cilt: 37 - Sayı: 4, 1129–1137. https://ajindex.com/articles/419112

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