Öz
Kaynakça
- Abdou, M. A., 2008. A generalized auxiliary equation method and its applications. Nonlinear Dynamics, 52(1-2): 95–102.
- Alhakim, L.A., Moussa, A.A., 2019. The double auxiliary equations method and its application to space-time fractional nonlinear equations. Journal of Ocean Engineering and Science, 4:7-13.
- Cenesiz, Y., Kurt, A., Tasbozan, O., 2017. On the New Solutions of the Conformable Time Fractional Generalized Hirota-Satsuma Coupled KdV System, Annals of West University of Timisoara-Mathematics and Computer Science, 55:37-50.
- Cenesiz, Y., Tasbozan, O., Kurt, A., 2017. Functional Variable Method for conformable fractional modified KdV-ZK equation and Maccari system. Tbilisi Mathematical Journal, 10(1): 118–126.
- Esen A. ve Tasbozan O., 2017. Numerical solution of time fractional Schrödinger equation by using quadratic B-spline finite elements, Annales Mathematicae Silesianae, 31: 83-98.
- Esen A., Karaagac B., Tasbozan O., 2017. Finite Difference Methods for Fractional Gas Dynamics Equation. Applied Mathematics & Information Sciences Letters, 4:1-4.
- Eslami, M., Rezazadeh, H., 2016. The first integral method for Wu–Zhang system with conformable time-fractional derivative. Calcolo, 53: 475–485.
- Jiong, S. ve Sirendaoreji, 2003. Auxiliary equation method for solving nonlinear partial differential equations. Physics Letters, 309:387-396.
- Khalil, R., Horani, M., Yousef, A., Sababheh, M., 2014. A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264:65-70.
- Korkmaz, A., Hosseini, K., 2017. Exact solutions of a nonlinear conformable time-fractional parabolic equation with exponential nonlinearity using reliable methods. Optical and Quantum Electronics, 49: 278.
- Taşbozan, O., Çenesiz, Y., Kurt, A., 2016. New solutions for conformable fractional Boussinesq and combined KdV-mKdV equations using Jacobi elliptic function expansion method. The European Physical Journal Plus, 131:244.
- Taşbozan, O., Bayaslı, G., 2018. Numerical Solutions of Conformable Partial Differential Equations By Homotopy Analysis Method. Afyon Kocatepe University Journal of Science and Engineering, 18: 842-851.
Yardımcı Denklem Yöntemi Yardımı ile Kesirli Mertebeden Kısmi Diferansiyel Denklemlerinin Analitik Çözümleri
Öz
Bu makalede conformable
kesirli mertebeden türev içeren lineer olmayan kesirli mertebeden
Konopelchenko-Dubrovsky ve Benjamin-Ono denklemlerinin analitik çözümleri yardımcı denklem
yöntemi ile elde edildi. Her iki denklem dalga dönüşümü yardımıyla lineer olmayan adi türevli
diferansiyel denkleme dönüştürüldükten sonra yardımcı denklem yöntemi
kullanıldı. Elde edilen çözümlerin üç boyutlu grafikleri verildi. Yardımcı
denklem yöntemi, diğer analitik yöntemlere göre daha çok analitik çözüm
içermektedir.
Anahtar Kelimeler
Conformable Diferansiyel Denklemler Yardımcı Denklem Yöntemi Kesirli Mertebeden Türev Analitik Yöntem Kesirli Mertebeden Konopelchenko-Dubrovsky Denklemi Kesirli Mertebeden Benjamin-Ono Denklemi
Kaynakça
- Abdou, M. A., 2008. A generalized auxiliary equation method and its applications. Nonlinear Dynamics, 52(1-2): 95–102.
- Alhakim, L.A., Moussa, A.A., 2019. The double auxiliary equations method and its application to space-time fractional nonlinear equations. Journal of Ocean Engineering and Science, 4:7-13.
- Cenesiz, Y., Kurt, A., Tasbozan, O., 2017. On the New Solutions of the Conformable Time Fractional Generalized Hirota-Satsuma Coupled KdV System, Annals of West University of Timisoara-Mathematics and Computer Science, 55:37-50.
- Cenesiz, Y., Tasbozan, O., Kurt, A., 2017. Functional Variable Method for conformable fractional modified KdV-ZK equation and Maccari system. Tbilisi Mathematical Journal, 10(1): 118–126.
- Esen A. ve Tasbozan O., 2017. Numerical solution of time fractional Schrödinger equation by using quadratic B-spline finite elements, Annales Mathematicae Silesianae, 31: 83-98.
- Esen A., Karaagac B., Tasbozan O., 2017. Finite Difference Methods for Fractional Gas Dynamics Equation. Applied Mathematics & Information Sciences Letters, 4:1-4.
- Eslami, M., Rezazadeh, H., 2016. The first integral method for Wu–Zhang system with conformable time-fractional derivative. Calcolo, 53: 475–485.
- Jiong, S. ve Sirendaoreji, 2003. Auxiliary equation method for solving nonlinear partial differential equations. Physics Letters, 309:387-396.
- Khalil, R., Horani, M., Yousef, A., Sababheh, M., 2014. A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264:65-70.
- Korkmaz, A., Hosseini, K., 2017. Exact solutions of a nonlinear conformable time-fractional parabolic equation with exponential nonlinearity using reliable methods. Optical and Quantum Electronics, 49: 278.
- Taşbozan, O., Çenesiz, Y., Kurt, A., 2016. New solutions for conformable fractional Boussinesq and combined KdV-mKdV equations using Jacobi elliptic function expansion method. The European Physical Journal Plus, 131:244.
- Taşbozan, O., Bayaslı, G., 2018. Numerical Solutions of Conformable Partial Differential Equations By Homotopy Analysis Method. Afyon Kocatepe University Journal of Science and Engineering, 18: 842-851.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Konular | Mühendislik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Aralık 2019 |
| Gönderilme Tarihi | 24 Eylül 2019 |
| Yayımlandığı Sayı | Yıl 2019 Cilt: 19 Sayı: 3 |
