A Robust Study on Atangana-Baleanu Fractional Coupled Burgers Equation

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Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi
Cilt: 8 Sayı: 5
A Robust Study on Atangana-Baleanu Fractional Coupled Burgers Equation

A Robust Study on Atangana-Baleanu Fractional Coupled Burgers Equation

Pages : 2464-2482

View : 42 | Download : 89

Publication Date : 2025-12-15

Article Type : Research Paper

Abstract :This study explores the application of the novel Atangana–Baleanu method to obtain highly accurate numerical solutions for coupled Burgers equation, which incorporates fractional derivatives in the sense of Atangana–Baleanu. To achieve this, the Atangana–Baleanu q-Elzaki homotopy analysis transform method (ABq-EHATM) is utilized as a computational technique to address the system effectively. This method uniquely combines the advantages of fractional calculus with the flexibility of q-Elzaki and homotopy analysis frameworks, offering a new perspective on handling nonlinearities and memory effects. A detailed investigation of the numerical solutions obtained through this hybrid approach is presented, emphasizing both the precision and computational efficiency of the proposed method. Furthermore, numerical simulations are carried out using Maple software for a range of fractional orders, allowing for a thorough examination of how variations in the fractional parameters influence the overall system dynamics. The results clearly demonstrate that the ABq-EHATM is not only an effective and flexible approach, but also a robust and reliable alternative for tackling complex. Overall, this study highlights a practical and innovative application of the ABq-EHATM, illustrating its potential benefits and underscoring its significance as a powerful tool in the field of fractional differential equation modeling.
Keywords : Atangana-Baleanu Elzaki dönüşümü, Burgers denklemi, Atangana-Baleanu q-Elzaki homotopi analiz dönüşümü yöntemi

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