Analytical solutions of conformable time, space, and time–space fractional KdV equations
Turkish Journal of Physics, cilt.42, sa.3, ss.254-264, 2018 (Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 42 Sayı: 3
- Basım Tarihi: 2018
- Doi Numarası: 10.3906/fiz-1711-17
- Dergi Adı: Turkish Journal of Physics
- Derginin Tarandığı İndeksler: Scopus, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.254-264
- Anahtar Kelimeler: KdV equation, conformable fractional KdV equation, conformable fractional calculus
- Kırklareli Üniversitesi Adresli: Evet
Özet
In this study, we consider the Korteweg–de Vries (KdV) equation for solitary waves in the domain of conformable fractional calculus. By means of this fractional theory, we obtain exact solutions for time, space, and time–space fractional KdV equations and demonstrate our results graphically according to the fractional order of the related equations. Furthermore, we report that the fractional order in the solution of the time fractional KdV equation is associated with viscosity of the medium by comparing three-dimensional picture presentations of solutions of time fractional KdV and Burgers–KdV equations.