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Journals / Bitlis Eren Üniversitesi Fen Bilimleri Dergisi / 2026 / Volume: 14 Issue: 3

The Novel Numerical Solutions of Conformable Fractional Navier-Stokes Equation with the Robust Method

Uyumlu Kesirli Navier-Stokes Denkleminin Güçlü Yöntemle Yeni Sayısal Çözümleri

Aslı Alkan(FIRAT ÜNİVERSİTESİ, FEN BİLİMLERİ ENSTİTÜSÜ, MATEMATİK (DR))0000-0002-1036-7178
Hasan Bulut(FIRAT ÜNİVERSİTESİ, FEN FAKÜLTESİ, MATEMATİK BÖLÜMÜ, MATEMATİK PR.)0000-0002-6089-1517
Tolga Aktürk(ORDU ÜNİVERSİTESİ, EĞİTİM FAKÜLTESİ, MATEMATİK VE FEN BİLİMLERİ EĞİTİMİ BÖLÜMÜ, MATEMATİK EĞİTİMİ ANABİLİM DALI)0000-0002-3948-6357
Pages
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Publication Date
2025-09-30
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AI Summary & Key Takeaways

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

This paper presents the conclusions derived from the numerical and graphical analysis.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, new numerical solutions of the conformable fractional Navier-Stokes equation are obtained by the conformable q-Shehu homotopy analysis transform method.
📊
Key Findings & Data:The fractional Navier-Stokes equation is an extension of the classical Navier-Stokes equations that incorporates fractional derivatives to account for complex flow behaviors such as memory effects and anomalous diffusion.
💡
Conclusion & Impact:This paper presents the conclusions derived from the numerical and graphical analysis.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Navier-Stokes equation · Conformable q-Shehu homotopy analysis transform method · Shehu transform

Abstract

In this study, new numerical solutions of the conformable fractional Navier-Stokes equation are obtained by the conformable q-Shehu homotopy analysis transform method. The fractional Navier-Stokes equation is an extension of the classical Navier-Stokes equations that incorporates fractional derivatives to account for complex flow behaviors such as memory effects and anomalous diffusion. It is particularly useful in describing fluid dynamics in non-Newtonian fluids, porous media, and other systems with intricate time or spatial dependencies. In addition, two and three-dimensional graphs of the obtained solutions were drawn. We also conduct an error analysis to evaluate the accuracy of the scheme. Computational simulations are performed to validate the accuracy of the upcoming method. This paper presents the conclusions derived from the numerical and graphical analysis.

Özet

Bu çalışmada, uyumlu kesirli Navier-Stokes denkleminin yeni sayısal çözümleri, uyumlu q-Shehu homotopi analiz dönüşümü yöntemi ile elde edilmiştir. Kesirli Navier-Stokes denklemi, hafıza etkileri ve anormal difüzyon gibi karmaşık akış davranışlarını hesaba katmak için kesirli türevleri içeren klasik Navier-Stokes denklemlerinin bir genişlemesidir. Özellikle Newton olmayan akışkanlar, gözenekli ortamlar ve karmaşık zaman veya mekansal bağımlılıklara sahip diğer sistemlerdeki akışkan dinamiğini tanımlamada faydalıdır. Ayrıca, elde edilen çözümlerin iki ve üç boyutlu grafikleri çizilmiştir. Ayrıca, şemanın doğruluğunu değerlendirmek için bir hata analizi yürütüyoruz. Yaklaşan yöntemin doğruluğunu doğrulamak için hesaplamalı simülasyonlar gerçekleştirilir. Bu makale, sayısal ve grafiksel analizden elde edilen sonuçları sunmaktadır.

🔖

Cite This Article

Alkan, A., Bulut, H., Aktürk, T. (2025). The Novel Numerical Solutions of Conformable Fractional Navier-Stokes Equation with the Robust Method. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, Volume: 14 Issue: 3. https://doi.org/10.17798/bitlisfen.1595852

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