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Journals / Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2018 / Cilt: 8 Sayı: 4

New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations

Orkun Taşbozan(Mustafa Kemal University, TURKEY)0000-0001-5003-6341
Ali Kurt(Mustafa Kemal University, TURKEY)0000-0002-0617-6037
Pages
295–303
Publication Date
2018-12-30
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AI Summary & Key Takeaways

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

These properties of conformable derivative superior to other popular definitions on obtaining analytical solutions of fractional equations.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, the authors discussed the new wave solutions of time-space fractional Liouville and Sine-Gordon equations by using a reliable analytical method called sub-equation method.
📊
Key Findings & Data:The fractional derivatives of considered equations are handled in conformable sense.
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Conclusion & Impact:These properties of conformable derivative superior to other popular definitions on obtaining analytical solutions of fractional equations.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Conformable Kesirli Türev · Liouville Denklemi · Sine Gordon Denklemi

Abstract

In this paper, the authors discussed the new wave solutions of time-space fractional Liouville and Sine-Gordon equations by using a reliable analytical method called sub-equation method. The fractional derivatives of considered equations are handled in conformable sense. Conformable derivative which is an easy and applicable type of fractional derivative, satisfies basic properties of known derivative with integer order such as Leibniz rule, quotient rule, chain rule. These properties of conformable derivative superior to other popular definitions on obtaining analytical solutions of fractional equations.

Özet

Bu makalede, yazarlar alt denklem yöntemi olarak adlandırılan güvenilir bir yöntem kullanarak zaman-uzay kesirli Lioville ve Sine-Gordon denklemlerinin yeni dalga çözümlerini elde ettiler. Kullanılan denklemlerde mevcut olan kesirli mertebeden türevler, conformable anlamında ele alınmıştır. Kolay, uıygulanabilir olan conformable türevi, bilinen türevin sağladığı Leibniz Kuralı, bölüm kuralı, zincir kuralı gibi kuralları sağlar. Bu özellikler conformable kesirli türeve diğer popüler türevler karşısında bir avantaj sağlamaktadır.

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Cite This Article

Taşbozan, O. (2018). New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations. Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 8 Sayı: 4, 295–303. https://doi.org/10.21597/jist.412948

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References (7)

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