Oransal Gecikmeli Uyumlu Zaman-Kesirli Mertebeden Genelleştirilmiş Burgers Denklemini Çözmek için Yeni Uyumlu Metotlar

Yıl 2023, Cilt: 39 Sayı: 2, 315 - 329, 31.08.2023

Halil Hüseyin Avcı , Halil Anaç

Öz

Bu makalede, uyumlu q-Mohand homotopi analiz dönüşüm yöntemi (Uq-MHADY) ve uyumlu Mohand Adomian ayrıştırma yöntemi (UMAAY) olarak adlandırılan iki yeni yöntem, oransal gecikmeli doğrusal olmayan uyumlu zaman-kesirli mertebeden genelleştirilmiş Burgers denkleminin yeni sayısal çözümlerini incelemek için kullanılmaktadır. Önerilen iki yeni yöntemden ilki olan Uq-MHADY, q-homotopi analiz dönüşüm yöntemi ile uyumlu Mohand dönüşümünün birleşiminden oluşan hibrit bir yöntemdir. Diğer yöntem olan CMADM ise Adomian ayrıştırma yöntemi ile uyumlu Mohand dönüşümünün birleşiminden oluşan hibrit bir yöntemdir. Önerilen yöntemlerin etkin çalıştığını ve güvenilir olduğunu göstermek için bilgisayar simülasyonları yapılmaktadır. Kesin çözümler bulunan çözümlerle karşılaştırıldığında, yeni tekniklerin her ikisinin de basit, güçlü ve oransal gecikmeli doğrusal olmayan uyumlu zaman-kesirli mertebeden kısmi diferansiyel denklemi çözmek için iyi çalıştığını görülmektedir.

Anahtar Kelimeler

Uyumlu zaman-kesirli mertebeden genelleştirilmiş Burgers denklemi, Uyumlu Mohand Adomian ayrıştırma metodu, Uyumlu Mohand dönüşümü

The New Conformable Methods to Solve Conformable Time- Fractional Generalized Burgers Equation with Proportional Delay

Öz

In this article, two novel methods called conformable q-Mohand homotopy analysis transform method (Cq-MHATM) and conformable Mohand Adomian decomposition method (CMADM) are utilized to examine the novel numerical solutions for nonlinear conformable time-fractional generalized Burgers equation with proportional delay. The first of the two new methods proposed, Cq-MHATM, is a hybrid method that combines q-homotopy analysis transform method and Mohand transform in the sense of comformable derivative. The other method, CMADM is also a hybrid method that combines Adomian decomposition method and Mohand transform in the sense of comformable derivative. The computer simulations were worked out to prove that the proposed methods work and are trusted. When the exact solutions are compared to the solutions that were found, it is seen that both of the new techniques are simple, powerful, and work well to solve nonlinear conformable time-fractional partial differential equation with proportional delay.

Anahtar Kelimeler

Conformable time-fractional generalized Burgers equation, Conformable Mohand Adomian decomposition method, Conformable Mohand transform

Kaynakça

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