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

Bu makalede, yazarlar alt denklem yöntemi olarak adlandırılan güvenilir bir yöntem kullanarak zaman-uzaykesirli Lioville ve Sine-Gordon denklemlerinin yeni dalga çözümlerini elde ettiler. Kullanılan denklemlerde mevcutolan kesirli mertebeden türevler, conformable anlamında ele alınmıştır. Kolay, uıygulanabilir olan conformabletürevi, bilinen türevin sağladığı Leibniz Kuralı, bölüm kuralı, zincir kuralı gibi kuralları sağlar. Bu özelliklerconformable kesirli türeve diğer popüler türevler karşısında bir avantaj sağlamaktadır.

Anahtar Kelimeler:

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

In this paper, the authors discussed the new wave solutions of time-space fractional Liouville andSine-Gordon equations by using a reliable analytical method called sub-equation method. The fractional derivativesof considered equations are handled in conformable sense. Conformable derivative which is an easy and applicabletype of fractional derivative, satisfies basic properties of known derivative with integer order such as Leibnizrule, quotient rule, chain rule. These properties of conformable derivative superior to other popular definitions onobtaining analytical solutions of fractional equations.

Keywords:

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

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