Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2018 / Cilt: 18 - Sayı: 3

Numerical Solutions of Conformable Partial Differential Equations By Homotopy Analysis Method

Conformable Kısmi Diferansiyel Denklemlerin Homotopi Analiz Yöntemi ile Nümerik Çözümleri

Pages
842–851
Publication Date
2022-10-12
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

The results were compared with analytical solutions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, the Homotopy Analysis Method (HAM) is applied to the fractional Wu-Zhang system and combined KdV-mKdV equation to obtain theirnumerical solutions.
📊
Key Findings & Data:In this paper, the Homotopy Analysis Method (HAM) is applied to the fractional Wu-Zhang system and combined KdV-mKdV equation to obtain theirnumerical solutions.
💡
Conclusion & Impact:The results were compared with analytical solutions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, the Homotopy Analysis Method (HAM) is applied to the fractional Wu-Zhang system and combined KdV-mKdV equation to obtain theirnumerical solutions. The results were compared with analytical solutions.

Özet

Bu makalede, kesirli Wu-Zhang sisteminin ve birleştirilmiş KdV-mKdV denklemi denkleminin nümerikçözümlerini elde etmek için Homotopi Analiz Yöntemi (HAM) uygulandı. Elde edilen sonuçlar, analitikçözümlerler ile karşılaştırıldı.

🔖

Cite This Article

TAŞBOZAN, O. (2022). Numerical Solutions of Conformable Partial Differential Equations By Homotopy Analysis Method. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 18 - Sayı: 3, 842–851. https://ajindex.com/articles/430167

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (9)

  1. Abbasbandy S., 2006. The application of homotopy analysis method to nonlinear equations arising in heat transfer. Physics Letters A, 360, 109–113.
  2. Abbasbandy S., Hashemi M.S. and Hashim I., 2013. On convergence of homotopy analysis method and its application to fractional integro-differential equations. Quaestiones Mathematicae, 36, 93-105.
  3. Çenesiz Y., Baleanu D., Kurt A. and Tasbozan O., 2016. New exact solutions of Burgers’ type equations with conformable derivative. Waves in Random and Complex Media, 27, 103-116.
  4. Çenesiz Y., Tasbozan O. and Kurt A., 2017. Functional Variable Method for conformable fractional modified KdV-ZK equation and Maccari system. Tbilisi Mathematical Journal,10, 117-125.
  5. Çenesiz Y., Tasbozan O. and Kurt A., 2017. On the New Solutions of the Conformable Time Fractional Generalized Hirota-Satsuma Coupled KdV System. Analele Universitatii de Vest, Timişoara Seria Matematica-Informatica LV, 55, 37- 49. Debnath L. and Bhatta D., 2007. Integral Transforms and Their Applications, Chapman-Hall/CRC, USA. Esen A., Tasbozan O. and Yagmurlu N. M., 2012. Approximate Analytical Solutions of the Fractional Sharma-Tasso-Olver Equation Using Homotopy Analysis Method and a Comparison with Other Methods. Çankaya University Journal of Science and Engineering, 9, 139-147.
  6. Esen A., Yagmurlu N. M. and Tasbozan O., 2013. Approximate Analytical Solution to Time-Fractional Damped Burger and Cahn-Allen Equations. Applied Mathematics & Information Sciences, 7, 1951-1956.
  7. Eslami, M. and Rezazadeh, H., 2016. The first integral method forWu–Zhang system with conformable time-fractional derivative. Calcolo, 53, 475–485.
  8. Eslami M. Rezazadeh H., Rezazadeh M. and Mosavi S.S., 2017. Exact solutions to the space–time fractional Schrödinger–Hirota equation and the space–time modified KDV- Zakharov–Kuznetsov equation. Optical and Quantum Electronics, 49, 279. Hilfer P., 2000. Various Approaches to the Fractional CalculusApplications of Fractional Calculus In Physics. World Scientific, Germany. Hosseini K., Bekir A. and Ansari R., 2017. New exact solutions of the conformable time-fractionalCahn– Allen and Cahn–Hilliard equations using the modified Kudryashov method. Optik, 132, 203-209.
  9. Hosseini K., Bejarbaneh E. Y., Bekir A. and Kaplan M., 2017. New exact solutions of some nonlinear evolution equations of pseudoparabolic type. Optical and Quantum Electronics, 49, 241. Iyiola O.S., Tasbozan O., Kurt A. and Çenesiz Y., 2017. On the analytical solutions of the system of c