The Efficient Robust Conformable Methods for Solving the Conformable Fractional Cahn-Allen Equation

Year 2024, Volume: 11 Issue: 2, 422 - 436, 29.11.2024

Özkan Avit , Halil Anaç

https://doi.org/10.35193/bseufbd.1360451

Abstract

This study focuses on the novel conformable methods employed to obtain new numerical solutions for the Cahn-Allen equation with conformable fractional derivatives. One of the two distinct methods put forth is the Cq-HATM, a hybrid technique that integrates the q-homotopy analysis transform method with the Laplace transform, utilizing the definition of conformable derivative. The CHPETM is a hybrid technique that combines the homotopy perturbation method with the Elzaki transform (ET). New numerical solutions of the conformal fractional differential Cahn-Allen equation were obtained using CHPETM and Cq-HATM. The computer simulations have been conducted in order to provide validation for the efficacy and reliability of the proposed methods. Upon performing a comparative analysis between the exact solutions and the solutions obtained through the novel methods, it becomes evident that both of these approaches exhibit simplicity, efficacy, and proficiency in addressing nonlinear conformable time-fractional coupled systems.

Keywords

Cahn-Allen equation, conformable homotopy perturbation Elzaki transform method, conformable Elzaki transform

Uyumlu Kesirli Mertebeden Cahn-Allen Denklemini Çözmek için Etkili Uyumlu Yöntemler

Abstract

Bu çalışma, uyumlu kesirli türevli Cahn-Allen denkleminin yeni sayısal çözümlerini elde etmek için kullanılan yeni uyumlu yöntemlere odaklanmaktadır. Öne sürülen iki farklı yöntemden biri, uyumlu kesirli türev tanımını kullanarak, q-homotopi analizi dönüşüm yöntemi ile Laplace dönüşümünün birleşiminden oluşan hibrit bir yöntem olan Uq-HADY' dir. UHPEDM, homotopi pertürbasyon yöntemininin Elzaki dönüşümüyle birleşiminden oluşan hibrit bir yöntemdir. Uyumlu kesirli türevli Cahn-Allen denkleminin yeni nümerik çözümleri UHPEDM ve Uq-HADY kullanılarak elde edilmiştir. Önerilen metodların etkinliğinin ve güvenilirliğinin doğrulanmasını sağlamak amacıyla bilgisayar simülasyonları yapılmıştır. Kesin çözümler ile yeni yöntemlerden elde edilen çözümler arasında karşılaştırma analizi yapıldığında, bu yaklaşımların her ikisinin de doğrusal olmayan uyumlu zaman-kesirli bağlı sistemleri ele almada basitlik, etkinlik ve yeterlilik sergiledikleri ortaya çıkmaktadır.

Keywords

Cahn-Allen denklemi, uyumlu homotopi pertürbasyon Elzaki dönüşüm metodu, uyumlu Elzaki dönüşümü

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