On the Solution of Burgers' Equation with the New Fractional Derivative
Open Physics, cilt.13, sa.1, ss.355-360, 2015 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 13 Sayı: 1
- Basım Tarihi: 2015
- Doi Numarası: 10.1515/phys-2015-0045
- Dergi Adı: Open Physics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.355-360
- Anahtar Kelimeler: Conformable Fractional Derivative, Homotopy Analysis Method, Hopf-Cole Transform, Time Fractional Burgers' Equation, Time Fractional Heat Equation
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Hatay Mustafa Kemal Üniversitesi Adresli: Evet
Özet
Firstly in this article, the exact solution of a time fractional Burgers' equation, where the derivative is conformable fractional derivative, with dirichlet and initial conditions is found byHopf-Cole transform. Thereafter the approximate analytical solution of the time conformable fractional Burger's equation is determined by using a Homotopy Analysis Method(HAM). This solution involves an auxiliary parameter which we also determine. The numerical solution of Burgers' equation with the analytical solution obtained by using the Hopf-Cole transform is compared.