The Novel Study on the Benjamin–Bona–Mahony Equation with Conformable Fractional Operator

Yıl 2025, Cilt: 13 Sayı: 3, 1040 - 1056, 31.07.2025

Hakkı Güngör

https://doi.org/10.29130/dubited.1549181

Öz

In this study, the conformable fractional Benjamin–Bona–Mahony (BBM) equation is solved by using the conformable q-formable homotopy analysis transform method (Cq-FHATM). This paper presents a practical implementation that demonstrates the possible advantages and effectiveness of the stated approach. In addition, an error analysis is undertaken to validate the scheme's precision. The accuracy of the method in the study is ensured by computational simulations. This study shows the findings obtained from numerical and graphical analysis. It also explains a computationally accurate and simple strategy to understand and solve complex phenomena in science and technology using compatible fractional nonlinear partial differential equations.

Anahtar Kelimeler

Benjamin-Bona-Mahony equation , formable transform , conformable fractional derivative

Etik Beyan

The authors declare no competing interests.

Uyumlu Kesirli Operatör ile Benjamin-Bona-Mahony Denklemi Üzerine Yeni Bir Çalışma

Öz

Bu çalışmada, uyumlu kesirli Benjamin-Bona-Mahony (BBM) denklemi, uyumlu q-oluşturulabilir homotopi analiz dönüşümü yöntemi (Cq-FHATM) kullanılarak çözülmüştür. Bu makale, önerilen tekniğin potansiyel faydalarını ve etkinliğini gösteren bir uygulama sunmaktadır. Ek olarak, şemanın hassasiyetini doğrulamak için bir hata analizi yapılmıştır. Çalışmadaki yöntemin doğruluğu, hesaplamalı simülasyonlarla sağlanmıştır. Bu çalışma, sayısal ve grafiksel analizden elde edilen bulguları göstermektedir. Ayrıca, uyumlu kesirli doğrusal olmayan kısmi diferansiyel denklemleri kullanarak bilim ve teknolojideki karmaşık fenomenleri anlamak ve çözmek için hesaplamalı olarak doğru ve basit bir strateji açıklamaktadır.

Anahtar Kelimeler

Benjamin-Bona-Mahony denklemi , şekillendirilebilir dönüşüm , uyumlu kesirli türev

Etik Beyan

Yazarlar hiçbir rakip çıkar beyan etmemektedir.

Kaynakça

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