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Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2020 / Cilt: 20 - Sayı: 2

Solution of Fractional Order Partial Differential Equations by Discrete Homotopy Perturbation Method

Kesirli Mertebe Kısmi Diferensiyel Denklemlerin Ayrık Homotopi Perturbasyon Metodu ile Çözümü

Figen ÖZPINAR
Pages
213–221
Publication Date
2022-10-12
DOI
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AI Summary & Key Takeaways

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

The method demonstrated in this study is expected to solve similar problems in fractional calculus.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This work is developed the discrete homotopy perturbation method with a space discrete version to solve the linear and nonlinear time derivative fractional partial differential equations.
📊
Key Findings & Data:The success and applicability of this method has been demonstrated by some sample problems.
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Conclusion & Impact:The method demonstrated in this study is expected to solve similar problems in fractional calculus.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

This work is developed the discrete homotopy perturbation method with a space discrete version to solve the linear and nonlinear time derivative fractional partial differential equations. The fractional derivatives are considered in the sense of Caputo. The success and applicability of this method has been demonstrated by some sample problems. When fractional order is unit, obtained results are good agreement with the exact solutions. The method demonstrated in this study is expected to solve similar problems in fractional calculus.

Özet

Bu çalışma, lineer ve lineer olmayan zaman kesirli mertebeli kısmi diferensiyel denklemleri çözmek içinayrık uzak biçimli ayrık homotopi perturbasyon metodunu geliştirmiştir. Kesirli mertebe türevler Caputoanlamında göz önüne alınmıştır. Bu metodun başarısı ve uygulanabilirliği bazı örnek problemler ilegösterilmiştir. Elde edilen sonuçlar kesirli mertebe bir olduğunda, tam çözümler ile iyi bir uyumlulukgöstermiştir. Bu çalışmada gösterilen metodun kesirli mertebe hesabındaki benzer problemleri çözmesibeklenmektedir.

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Cite This Article

ÖZPINAR, F. (2022). Solution of Fractional Order Partial Differential Equations by Discrete Homotopy Perturbation Method. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 20 - Sayı: 2, 213–221. https://ajindex.com/articles/429812

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References (4)

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