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Dergiler / Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2026 / Cilt: 11 Sayı: 1

The Double (G^( ^' )/G,1/G)-Expansion Method and Its Applications for Some Nonlinear Partial Differential Equations

Mustafa Ekici(UŞAK ÜNİVERSİTESİ, EĞİTİM FAKÜLTESİ)0000-0003-2494-8229
Metin Ünal(UŞAK ÜNİVERSİTESİ, EĞİTİM FAKÜLTESİ)0000-0002-4462-0872
Sayfa
599–608
Yayın Tarihi
2021-03-01
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

These solutions can be shown in terms of trigonometric, hyperbolic and rational functions.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The double (G^( ^' )/G,1/G)-expansion method is used to find exact travelling wave solutions to the fractional differantial equations in the sense of Jumarie’s modified Riemann- Liouville derivative.
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Temel Bulgular & Veri:We exploit this method for the combined KdV- negative-order KdV equation (KdV-nKdV) and the Calogero-Bogoyavlinskii-Schiff equation (CBS) of fractional order.
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Sonuç & Katkı:These solutions can be shown in terms of trigonometric, hyperbolic and rational functions.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:The double expansion method · the Calogero–Bogoyavlinskii–Schiff equation · the combined KdV- negative-order KdV equation

Özet

The double (G^( ^' )/G,1/G)-expansion method is used to find exact travelling wave solutions to the fractional differantial equations in the sense of Jumarie’s modified Riemann- Liouville derivative. We exploit this method for the combined KdV- negative-order KdV equation (KdV-nKdV) and the Calogero-Bogoyavlinskii-Schiff equation (CBS) of fractional order. We see that these solutions are concise and easy to understand the physical phenomena of the nonlinear partial differential equations. These solutions can be shown in terms of trigonometric, hyperbolic and rational functions.

Abstract

The double (G^( ^' )/G,1/G)-expansion method is used to find exact travelling wave solutions to the fractional differantial equations in the sense of Jumarie’s modified Riemann- Liouville derivative. We exploit this method for the combined KdV- negative-order KdV equation (KdV-nKdV) and the Calogero-Bogoyavlinskii-Schiff equation (CBS) of fractional order. We see that these solutions are concise and easy to understand the physical phenomena of the nonlinear partial differential equations. These solutions can be shown in terms of trigonometric, hyperbolic and rational functions.

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Bu Makaleye Atıf Yap

Ekici, M., Ünal, M. (2021). The Double (G^( ^' )/G,1/G)-Expansion Method and Its Applications for Some Nonlinear Partial Differential Equations. Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 11 Sayı: 1, 599–608. https://doi.org/10.21597/jist.767930

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