Atangana-Baleanu Caputo Anlamında Üçüncü Mertebeden Kesirli Türevli Diferansiyel Denklemler için Implicit Rather Fark Metodu

Year 2020, Volume: 7 Issue: 2, 952 - 959, 30.12.2020

Mahmut Modanlı Sümeyye Eker

https://doi.org/10.35193/bseufbd.722419

Cited By: 1

Abstract

Atangana-Baleanu Caputo (ABC) türevi ile tanımlı üçüncü mertebeden kesirli kısmi diferansiyel denklemin tam çözümü başlangıç ve sınır değerlerine bağlı olarak hesaplandı. Bu denklem için kararlılık kestirimleri verildi. Bu denklem Implicit Rather fark metodu ile çözüldü. Problem için fark şemalarının kararlılığı gösterildi. Bu teknik ABC üçüncü mertebeden kısmi diferansiyel denklemin α=0.001,0.1,0.5,0.99,0.999 için kesirli türev değerlerine karşılık uygulanmıştır. Yaklaşık çözüm, tekniğin doğruluğunu ve etkinliğini onaylar.

Keywords

Kesirli Diferansiyel Denklemi, Implicit Rather Fark Şeması, Kararlılık Kestirimi, Yaklaşık Çözüm, Tam Çözüm

Implicit Rather Difference Method for Third Order Differential Equations in the Sense of Atangana-Baleanu Caputo Fractional Derivative

Abstract

The exact solution of the third order partial differential equation defined by Atangana-Baleanu Caputo (ABC) fractional derivative is calculated for depending on the initial and boundary values. Stability estimates are obtained for this equation. Implicit Rather difference schemes are constructed for this problem. The stability of difference schemes for this problem is presented. This technique has been applied by ABC fractional orders α=0.001,0.1,0.5,0.99,0.999. Approximation solution confirms the accuracy and effectiveness of the technique.

Keywords

Fractional Differential Equation, Implicit Rather Difference Schemes, Stability Estimates, Approximation Solution, Exact Solution

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