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Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2019 / Cilt: 19 - Sayı: 3

Analytical Solutions of Fractional Order Partial Diferantial Equations with the Help of Auxiulary Equation Method

Yardımcı Denklem Yöntemi Yardımı ile Kesirli Mertebeden Kısmi Diferansiyel Denklemlerinin Analitik Çözümleri

Sera YILMAZ
Orkun TAŞBOZAN
Pages
626–634
Publication Date
2022-10-12
DOI
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AI Summary & Key Takeaways

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

The auxiliary equation method contains more analytical solutions than other analytical methods.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this article, the analytical solutions of nonlinear fractional order Konopelchenko-Dubrovsky and Benjamin-Ono equations are obtained with the aid of auxiulary equation method where the fractional derivatives are in conformable sense.
📊
Key Findings & Data:After both equations were converted to nonlinear ordinary differential equations with the help of wave transformation, auxiliary equation method was used.
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Conclusion & Impact:The auxiliary equation method contains more analytical solutions than other analytical methods.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this article, the analytical solutions of nonlinear fractional order Konopelchenko-Dubrovsky and Benjamin-Ono equations are obtained with the aid of auxiulary equation method where the fractional derivatives are in conformable sense. After both equations were converted to nonlinear ordinary differential equations with the help of wave transformation, auxiliary equation method was used. Three dimensional graphics of the obtained results are given. The auxiliary equation method contains more analytical solutions than other analytical methods.

Özet

Bu makalede conformable kesirli mertebeden türev içeren lineer olmayan kesirli mertebedenKonopelchenko-Dubrovsky ve Benjamin-Ono denklemlerinin analitik çözümleri yardımcı denklemyöntemi ile elde edildi. Her iki denklem dalga dönüşümü yardımıyla lineer olmayan adi türevlidiferansiyel denkleme dönüştürüldükten sonra yardımcı denklem yöntemi kullanıldı. Elde edilençözümlerin üç boyutlu grafikleri verildi. Yardımcı denklem yöntemi, diğer analitik yöntemlere göre dahaçok analitik çözüm içermektedir.

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Cite This Article

YILMAZ, S., TAŞBOZAN, O. (2022). Analytical Solutions of Fractional Order Partial Diferantial Equations with the Help of Auxiulary Equation Method. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 19 - Sayı: 3, 626–634. https://ajindex.com/articles/429884

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