Zaman Konum Kesirli Liouville ve Sine-Gordon Denklemlerinin Yeni Dalga Çözümleri

Year 2018, Volume: 8 Issue: 4, 295 - 303, 30.12.2018

Orkun Taşbozan Ali Kurt

https://doi.org/10.21597/jist.412948

Cited By: 3

Abstract

Bu makalede, yazarlar alt denklem yöntemi olarak adlandırılan güvenilir bir yöntem kullanarak zaman-uzay

kesirli Lioville ve Sine-Gordon denklemlerinin yeni dalga çözümlerini elde ettiler. Kullanılan denklemlerde mevcut

olan kesirli mertebeden türevler, conformable anlamında ele alınmıştır. Kolay, uıygulanabilir olan conformable

türevi, bilinen türevin sağladığı Leibniz Kuralı, bölüm kuralı, zincir kuralı gibi kuralları sağlar. Bu özellikler

conformable kesirli türeve diğer popüler türevler karşısında bir avantaj sağlamaktadır.

Keywords

Conformable Kesirli Türev, Liouville Denklemi, Sine Gordon Denklemi, Dalga Çözümü, Alt Denklem Yöntemi, Alt Denklem Yöntemi

New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations

Abstract

In this paper, the authors discussed the new wave solutions of time-space fractional Liouville and

Sine-Gordon equations by using a reliable analytical method called sub-equation method. The fractional derivatives

of considered equations are handled in conformable sense. Conformable derivative which is an easy and applicable

type of fractional derivative, satisfies basic properties of known derivative with integer order such as Leibniz

rule, quotient rule, chain rule. These properties of conformable derivative superior to other popular definitions on

obtaining analytical solutions of fractional equations.

Keywords

Conformable fractional derivative, Sine-Gordon, Wave Solutions, Sub-Equation method; Liouville equation

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