Lineer Olmayan Uzay – Zaman Kesirli Diferensiyel Denklem Sistemlerinin Soliter Dalga ve Diğer Çözümleri

Year 2018, Volume: 8 Issue: 2, 515 - 522, 01.06.2018

Murat Koparan Özkan Güner

Abstract

Bu çalışmada, G Gl b l -açılım metodu kullanarak kesir mertebeli Boussinesq denklem sistemleri ve kesirli iki boyutlu Burgers’ denklemlerinin bazı hareketli dalga çözümleri elde edilmiştir. Bu tam çözümler hiperbolik, trigonometrik ve rasyonel fonksiyon çözümlerini içermektedir. Kesirli karmaşık dönüşüm, genellikle, modifiye Riemann-Liouville türevi içeren kesirli kısmi diferansiyel denklemi adi diferensiyel denkleme dönüştürmek için kullanılır. Düşünülen dönüşüm ve metodun, diğer lineer olmayan kesir mertebeli denklemlerin ve sistemlerin çözümünde güvenilir, verimli ve etkili bir yol olduğu gösterilmiştir.

Keywords

b l -açılım metodu, Tam çözüm, Kesir mertebeli variant Boussinesq denklem sistemi, İki boyutlu kesir mertebeli Burger denklem sistemi

Solitary Wave and other Solutions of Nonlinear Space-Time Fractional Differential Equation Systems

Abstract

In this study, we have successfully found some travelling wave solutions of the variant Boussinesq system and fractional system of two-dimensional Burgers' equations of fractional order by using the -expansion method. These exact solutions contain hyperbolic, trigonometric and rational function solutions. The fractional complex transform is generally used to convert a partial fractional differential equation FDEs with modified Riemann-Liouville derivative into ordinary differential equation. We showed that the considered transform and method are very reliable, efficient and powerful in solving wide classes of other nonlinear fractional order equations and systems.

Keywords

The G&#039, /G -expansion method, exact solution, fractional order system of variant Boussinesq equations, fractional system of two-dimensional Burgers&#039, equations

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