A Robust Study on Atangana-Baleanu Fractional Coupled Jaulent-Miodek System

Hakkı Güngör

doi:10.31466/kfbd.1717803

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Atangana–Baleanu Kesirli Bağlantılı Jaulent–Miodek Sistemi Üzerine Kapsamlı Bir Çalışma

Abstract

Bu çalışma, kuramsal temelleri, hesaplamalı yönleri ve pratik etkinliği çerçevesinde Atangana–Baleanu kesirli türevinin, eşlenik Jaulent–Miodek sistemi bağlamındaki kullanımını incelemektedir. Mittag–Leffler çekirdeği ile karakterize edilen Atangana–Baleanu operatörü, güçlü bellek etkileri ve karmaşık zamansal davranış sergileyen sistemlerin modellenmesinde esnek bir yaklaşım sunmaktadır. Eşlenik Jaulent–Miodek sistemi ise, farklı dalga yapıları arasındaki etkileşimleri tanımlamak amacıyla yaygın olarak kullanılan, iyi bilinen bir doğrusal olmayan dalga denklemleri sınıfını temsil etmektedir. Ancak klasik formülasyonlar, bellek etkisi ve uzun vadeli süreçlerin etkisini yakalamada çoğu zaman yetersiz kalmaktadır. Bu zorlukların üstesinden gelmek amacıyla, Atangana–Baleanu türevinin entegrasyonu, söz konusu dinamikleri daha iyi modellemek için önerilmiştir. Bu çalışmada, Jaulent–Miodek sisteminin ayrıntılı yapısal özelliklerinin Atangana–Baleanu çerçevesiyle ne denli etkin bir biçimde ele alındığı hem kuramsal analizler hem de sayısal benzetimler aracılığıyla ortaya konmuştur. Elde edilen bulgular, bu kesirli türevin karmaşık fiziksel olayların incelenmesinde kesirli hesaplamaların uygulama alanlarını genişletme potansiyelini vurgulamaktadır.

Keywords

Jaulent–Miodek Sistemi, Atangana–Baleanu q-Elzaki homotopi analiz dönüşüm yöntemi, Atangana–Baleanu Elzaki dönüşümü

A Robust Study on Atangana-Baleanu Fractional Coupled Jaulent-Miodek System

Abstract

This study explores the use of the Atangana–Baleanu fractional derivative within the context of the coupled Jaulent–Miodek system, with a focus on its theoretical foundations, computational aspects, and practical effectiveness. The Atangana–Baleanu operator, characterized by its Mittag–Leffler kernel, offers a flexible approach to modeling systems that exhibit strong memory effects and complex temporal behavior. The coupled Jaulent–Miodek system itself represents a well-known class of nonlinear wave equations and is widely used to describe interactions between different wave structures. However, classical formulations often fall short in capturing the influence of memory and long-term processes. To overcome these challenges, the integration of the Atangana–Baleanu derivative has been proposed as a way to better model such dynamics. In this work, both theoretical analysis and numerical simulations are carried out to show how effectively the Atangana–Baleanu framework handles the detailed structural features of the Jaulent–Miodek system. The findings further emphasize the potential of this fractional derivative in broadening the applications of fractional calculus in the study of complex physical phenomena.

Keywords

Jaulent-Miodek System, Atangana-Baleanu q-Elzaki homotopy analysis transform method, Atangana-Baleanu Elzaki transform

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Details

Primary Language

English

Subjects

Classical Physics (Other)

Journal Section

Research Article

Authors

Hakkı Güngör ^*
0000-0002-9546-665X
Türkiye

Publication Date

May 12, 2026

Submission Date

June 12, 2025

Acceptance Date

November 24, 2025

Published in Issue

Year 2026 Volume: 16 Number: 2

DOI

https://doi.org/10.31466/kfbd.1717803

IZ

https://izlik.org/JA72XM93HH

APA

Güngör, H. (2026). A Robust Study on Atangana-Baleanu Fractional Coupled Jaulent-Miodek System. Karadeniz Fen Bilimleri Dergisi, 16(2), 671-688. https://doi.org/10.31466/kfbd.1717803

AMA

1.Güngör H. A Robust Study on Atangana-Baleanu Fractional Coupled Jaulent-Miodek System. KFBD. 2026;16(2):671-688. doi:10.31466/kfbd.1717803

Chicago

Güngör, Hakkı. 2026. “A Robust Study on Atangana-Baleanu Fractional Coupled Jaulent-Miodek System”. Karadeniz Fen Bilimleri Dergisi 16 (2): 671-88. https://doi.org/10.31466/kfbd.1717803.

EndNote

Güngör H (May 1, 2026) A Robust Study on Atangana-Baleanu Fractional Coupled Jaulent-Miodek System. Karadeniz Fen Bilimleri Dergisi 16 2 671–688.

IEEE

[1]H. Güngör, “A Robust Study on Atangana-Baleanu Fractional Coupled Jaulent-Miodek System”, KFBD, vol. 16, no. 2, pp. 671–688, May 2026, doi: 10.31466/kfbd.1717803.

ISNAD

Güngör, Hakkı. “A Robust Study on Atangana-Baleanu Fractional Coupled Jaulent-Miodek System”. Karadeniz Fen Bilimleri Dergisi 16/2 (May 1, 2026): 671-688. https://doi.org/10.31466/kfbd.1717803.

JAMA

1.Güngör H. A Robust Study on Atangana-Baleanu Fractional Coupled Jaulent-Miodek System. KFBD. 2026;16:671–688.

MLA

Güngör, Hakkı. “A Robust Study on Atangana-Baleanu Fractional Coupled Jaulent-Miodek System”. Karadeniz Fen Bilimleri Dergisi, vol. 16, no. 2, May 2026, pp. 671-88, doi:10.31466/kfbd.1717803.

Vancouver

1.Hakkı Güngör. A Robust Study on Atangana-Baleanu Fractional Coupled Jaulent-Miodek System. KFBD. 2026 May 1;16(2):671-88. doi:10.31466/kfbd.1717803

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Atangana–Baleanu Kesirli Bağlantılı Jaulent–Miodek Sistemi Üzerine Kapsamlı Bir Çalışma

Abstract

Keywords

A Robust Study on Atangana-Baleanu Fractional Coupled Jaulent-Miodek System

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

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