Year 2020, Volume 7 , Issue 2, Pages 952 - 959 2020-12-30

Atangana-Baleanu Caputo Anlamında Üçüncü Mertebeden Kesirli Türevli Diferansiyel Denklemler için Implicit Rather Fark Metodu
Implicit Rather Difference Method for Third Order Differential Equations in the Sense of Atangana-Baleanu Caputo Fractional Derivative

Mahmut MODANLI [1] , Sümeyye EKER [2]


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.

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.

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Primary Language en
Subjects Basic Sciences
Journal Section Articles
Authors

Orcid: 0000-0002-7743-3512
Author: Mahmut MODANLI (Primary Author)
Institution: HARRAN UNIVERSITY
Country: Turkey


Orcid: 0000-0001-7278-4711
Author: Sümeyye EKER
Institution: T.C. MİLLİ EĞİTİM BAKANLIĞI
Country: Turkey


Dates

Application Date : April 17, 2020
Acceptance Date : September 30, 2020
Publication Date : December 30, 2020

APA Modanlı, M , Eker, S . (2020). Implicit Rather Difference Method for Third Order Differential Equations in the Sense of Atangana-Baleanu Caputo Fractional Derivative . Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi , 7 (2) , 952-959 . DOI: 10.35193/bseufbd.722419