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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
Ahmet Doğan DEMİRHAN
Fevzi BÜYÜKKILIÇ
Pages
254–264
DOI
—
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AI Summary & Key Takeaways

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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 equation is associated with viscosity of the medium by comparing three-dimensional picture presentations of solutions of time fractional 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 of conformable fractional calculus.
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Key Findings & Data:By means of this fractional theory, we obtain exact solutions for time, space, and time-space fractional KdV equations and demonstrate our results graphically according to the fractional order of the related equations.
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Conclusion & Impact:Furthermore, we report that the fractional order in the solution of the time fractional KdV equation is associated with viscosity of the medium by comparing three-dimensional picture presentations of solutions of time fractional KdV and Burgers-KdV equations.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:KdV equation · conformable fractional KdV equation · conformable fractional calculus

Abstract

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

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Cite This Article

KARAYER, H. H., DEMİRHAN, A. D., BÜYÜKKILIÇ, F. (2018). 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/377831

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