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

Year 2020, Volume: 20 Issue: 2, 213 - 221, 20.05.2020

Figen Özpınar

https://doi.org/10.35414/akufemubid.685429

Cited By: 2

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.

Keywords

Discrete homotopy perturbation method, Caputo fractional derivative, Fractional discrete diffusion equation, Fractional discrete Schrödinger equation, Fractional discrete Burgers’ equation

Kesirli Mertebe Kısmi Diferensiyel Denklemlerin Ayrık Homotopi Perturbasyon Metodu ile Çözümü

Abstract

Bu çalışma, lineer ve lineer olmayan zaman kesirli mertebeli kısmi diferensiyel denklemleri çözmek için ayrık uzak biçimli ayrık homotopi perturbasyon metodunu geliştirmiştir. Kesirli mertebe türevler Caputo anlamında göz önüne alınmıştır. Bu metodun başarısı ve uygulanabilirliği bazı örnek problemler ile gösterilmiştir. Elde edilen sonuçlar kesirli mertebe bir olduğunda, tam çözümler ile iyi bir uyumluluk göstermiştir. Bu çalışmada gösterilen metodun kesirli mertebe hesabındaki benzer problemleri çözmesi beklenmektedir.

Keywords

Ayrık homotopi perturbasyon metodu, Caputo kesirli mertebe türev, Kesirli mertebe ayrık difüzyon denklemi, Kesirli mertebe ayrık Schrödinger denklemi, Kesirli mertebe ayrık Burgers denklemi

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