Atangana Konformal Türevli Modifiye Camassa-Holm ve Degasperis-Procesi Denklemlerinin Yeni Dalga Çözümlerinin Elde Edilmesi

Year 2024, Volume: 24 Issue: 4, 819 - 828, 20.08.2024

Özlem Kırcı

https://doi.org/10.35414/akufemubid.1398202

Abstract

Bu çalışmada, akışkanlar mekaniği, hidrodinamik ve fiber optik alanlarında birçok fiziksel olayı tanımlamak için sıkça kullanılması nedeni ile zaman-kesirli modifiye Camassa-Holm (mCH) ve zaman-kesirli modifiye Degasperis-Procesi (mDP) denklemlerinin yeni tam çözümlerinin elde edilmesi amaçlanmıştır. Bu kesirli denklemler, Atangana konformal türevi göz önüne alınarak nonlineer adi diferansiyel denklemlere dönüştürülmüştür. Kesirli evolüsyon denklemlerinin istenen tam çözümlerini elde etmek için bu nonlineer adi diferansiyel denklemlere (m+1/G’)-genişleme metodu uygulanmıştır. Hesaplamalar Mathematica yazılım sistemi ile gerçekleştirilmiştir. Ayrıca bu çalışmada sunulan çözümler literatürde zaman-kesirli CH ve DP denklemleri için elde edilen çözümler ile kıyaslanmış ve çözümlerin davranışları grafiksel olarak sunulmuştur.

Keywords

Camassa-Holm ve Degasperis-Procesi denklemleri, (m+1/G')-genişleme yöntemi, Atangana konformal türevi

Construction of the New Wave Solutions of Modified Camassa-Holm and Degasperis-Procesi Equations with Atangana’s Conformable Derivative

Abstract

In this study it is aimed to expose the new exact wave solutions of time-fractional modified Camassa-Holm (mCH) and time-fractional modified Degasperis-Procesi (mDP) equations due to being extensively used to delineate many physical phenomena in fluid mechanics, hydrodynamics and optical fibers. The aforementioned fractional equations are transformed into nonlinear ordinary differential equations (NLODE) considering the Atangana’s conformable derivative (ACD). Then the (m+1/G’)-expansion method is applied for these NLODEs to obtain the desired exact solutions of the fractional evolution equations. The evaluations are fulfilled through the software system Mathematica. Also the reported solutions in this manuscript are compared with the ones in the literature for the time-fractional CH and DP equations and the behaviors of the solutions are presented graphically.

Keywords

Camassa-Holm and Degasperis-Procesi equations, (m+1/G’)-expansion method, Atangana’s conformable derivative

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