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Journals / Turkish Journal of Physics / 2018 / Cilt: 42 - Sayı: 3

Analytical solutions of conformable time, space, and time–space fractional KdV equations

Hasibe Hale KARAYER
Fevzi BÜYÜKKILIÇ
Ahmet Doğan DEMİRHAN
Pages
254–264
Publication Date
2022-11-05
DOI
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⚡ TL;DR(Too Long; Didn't Read)

Furthermore, we report that the fractional order in the solution of the time fractional KdV equationis associated with viscosity of the medium by comparing three-dimensional picture presentations of solutions of timefractional KdV and Burgers–KdV equations.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we consider the Korteweg–de Vries (KdV) equation for solitary waves in the domain ofconformable fractional calculus.
📊
Key Findings & Data:By means of this fractional theory, we obtain exact solutions for time, space, andtime–space fractional KdV equations and demonstrate our results graphically according to the fractional order of therelated equations.
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Conclusion & Impact:Furthermore, we report that the fractional order in the solution of the time fractional KdV equationis associated with viscosity of the medium by comparing three-dimensional picture presentations of solutions of timefractional KdV and Burgers–KdV equations.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study, we consider the Korteweg–de Vries (KdV) equation for solitary waves in the domain ofconformable fractional calculus. By means of this fractional theory, we obtain exact solutions for time, space, andtime–space fractional KdV equations and demonstrate our results graphically according to the fractional order of therelated equations. Furthermore, we report that the fractional order in the solution of the time fractional KdV equationis associated with viscosity of the medium by comparing three-dimensional picture presentations of solutions of timefractional KdV and Burgers–KdV equations.

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Cite This Article

KARAYER, H. H., BÜYÜKKILIÇ, F., DEMİRHAN, A. D. (2022). Analytical solutions of conformable time, space, and time–space fractional KdV equations. Turkish Journal of Physics, Cilt: 42 - Sayı: 3, 254–264. https://ajindex.com/articles/613981

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