Exact Solutions of Conformable Differential Equations Using Generalized Kudryashov Method

Abstract

Nonlinear conformable differential equations have an important place in mathematical physics. Recently, the search for exact solutions of these equtions has been an appealing field for most scientists. In this work, exact solutions of the conformable third-order modified KdV equation and conformable Boussinesq equation founded by using the generalized Kudryashov method. This method is an effective method to acquire exact solutions of nonlinear conformable equations. All calculations in this study have been made and checked back with the aid of the Maple packet program. Also, the graphical representation of the obtained solutions is given. The obtained solutions in this manuscript have the potential to be useful in mathematical physics and engineering.

Keywords

• Exact solutions
• Generalized Kudryashov method
• Symbolic computation
• Conformable time fractional third order modified KdV equation
• Conformable time fractional Boussinesq equation

Conformable Diferensiyel Denklemlerin Genelleştirilmiş Kudryashov Yöntemiyle Tam Çözümleri

Abstract

Lineer olmayan conformable diferensiyel denklemler matematiksel fizikte önemli bir yere sahiptir. Bu denklemlerin tam çözümlerinin elde edilmesi, son yıllarda oldukça ilgi çeken bir çalışma alanı olarak karşımıza çıkmaktadır. Bu makalede, conformable üçüncü mertebeden modifiye KdV denklemi ve conformable Boussinesq denkleminin tam çözümleri genelleştirilmiş Kudryashov yöntemi kullanılarak bulunmuştur. Bu yöntem, lineer olmayan conformable denklemlerin tam çözümlerini elde etmede kullanılan etkili bir yöntemdir. Bu çalışmadaki bütün hesaplamalar Maple paket programı kullanılarak yapılmış ve elde edilen çözümler denklemlerde yerine konularak doğruluğu teyit edilmiştir. Ayrıca elde edilen çözümlerin grafiklerine de yer verilmiştir. Elde edilen çözümler, matematiksel fizik ve mühendislik alanlarında önemli kullanım alanlarına sahip olma potansiyeline sahiptirler.

Keywords

• Tam Çözümler,
• Genelleştirilmiş Kudryashov metot,
• Sembolik Hesaplama,
• Conformable zaman kesir mertebeli üçüncü mertebeden modifiye KdV denklemi,
• Conformable zaman kesir mertebeli Boussinesq denklemi

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