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Journals / Universal Journal of Mathematics and Applications / 2019 / Cilt: 2 - Sayı: 2

The Existence and Uniqueness of Initial-Boundary Value Problems of the Fractional Caputo-Fabrizio Differential Equations

Şuayip TOPRAKSEVEN
Pages
100–106
Publication Date
2019-06-28
DOI
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AI Summary & Key Takeaways

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

An application to mass spring damper system for this new fractional derivative has also been presented in details.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, the existence and uniqueness problem of the initial and boundary value problems of the linear fractional Caputo-Fabrizio differential equation of order $\sigma \in (1,2]$ have been investigated.
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Key Findings & Data:By using the Laplace transform of the fractional derivative, the fractional differential equations turn into the classical differential equation of integer order.
💡
Conclusion & Impact:An application to mass spring damper system for this new fractional derivative has also been presented in details.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Caputo–Fabrizio fractional derivative · Existence and uniqueness of fractional differential equations · Laplace transform

Abstract

In this paper, the existence and uniqueness problem of the initial and boundary value problems of the linear fractional Caputo-Fabrizio differential equation of order $\sigma \in (1,2]$ have been investigated. By using the Laplace transform of the fractional derivative, the fractional differential equations turn into the classical differential equation of integer order. Also, the existence and uniqueness of nonlinear boundary value problem of the fractional Caputo-Fabrizio differential equation has been proved. An application to mass spring damper system for this new fractional derivative has also been presented in details.

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Cite This Article

TOPRAKSEVEN, Ş. (2019). The Existence and Uniqueness of Initial-Boundary Value Problems of the Fractional Caputo-Fabrizio Differential Equations. Universal Journal of Mathematics and Applications, Cilt: 2 - Sayı: 2, 100–106. https://ajindex.com/articles/819974

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