Araştırma Makalesi
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Yıl 2018, Cilt 42, Sayı 3, 254 - 264, 01.06.2018

Öz

Kaynakça

  • Grimshaw, R. H. J. Solitary Waves in Fluids ; WIT Press: Southampton, UK, 2007.
  • Brauer, K. The Korteweg-de Vries equation: history, exact solutions, and graphical representation . University of Osnabruck, 2006.
  • Taha, T. R.; Ablowitz, M. J. J. Comput. Phys. 1984 , 55 , 231-253.
  • Momani, S. Math. Comput. Simulation 2005 , 70 , 110-118.
  • El-Wakil, S. A.; Abulwafa, E. M.; Zahran, M. A.; Mahmoud, A. A. Nonlinear Dyn. 2011 , 65 , 55-63.
  • Zhang, Y. Electron. J. Differ. Equ. 2014 , 2014 , 1-12.
  • Ganji, Z. Z.; Ganji, D. D.; Rostamiyan, Y. Appl. Math. Model. , 2009 , 33 , 3107-3113.
  • Machado, J. A. T.; Silva, M. F.; Barbosa, R. S.; Jesus, I. S.; Reis, C. M.; Marcos, M. G.; Galhano, A. F. Math. Prob. Eng. 2010 , 2010 , 1-34.
  • Sierociuk, D.; Dzielinski, A.; Sarwas, G.; Petras, I.; Podlubny, I.; Skovranek, T. Phil. Trans. R. Soc. A. 2012 , 371 , 1-10.
  • Podlubny, I. Fractional Differential Equations ; Academic Press: New York, NY, USA, 1999.
  • He, J. H; Wu, X. H. Comput. Math. Appl. 2007 , 54 , 881-894.
  • Adomian, G. J. Math. Anal. Appl. 1988 , 135 , 501-544.
  • Khalil, R.; Horani, M. A.; Yousef, A.; Sababheh, M. J. Comput. Appl. Math. 2014 , 264 , 65-70.
  • Abdaljawad, T. J. Comput. Appl. Math. 2014 , 279 , 57-66.
  • Anderson, D. R.; Ulness, D. J. J. Math. Phy. 2015 , 56 , 1-18.
  • Eslami, M. Appl. Math. Comput. 2016 , 285 , 141-148.
  • Karayer, H.; Demirhan, D.; Buyukkilic, F. Commun. Theor. Phys. . 2016 , 66 , 12-18.
  • Ortigueira, M. D.; Machado, J. A. T. J. Comput. Phys. 2015 , 293 , 4-13.
  • Iyiola, O. S.; Tasbozan, O,; Kurt, A.; Cenesiz, Y. Chaos Solitons Fractals 2017 , 94 , 1-7.
  • Eslami, M.; Rezazadeh, H. Calcolo 2016 , 1-11.
  • Feng, Z.; Meng, Q. Sci. China Ser. A 2007 , 50 , 412-422.
  • Shu, J. J. J. Phys. A Math. Gen. 1987 , 20 , 49-56.

Analytical solutions of conformable time, space, and time–space fractional KdV equations

Yıl 2018, Cilt 42, Sayı 3, 254 - 264, 01.06.2018

Öz

  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.

Kaynakça

  • Grimshaw, R. H. J. Solitary Waves in Fluids ; WIT Press: Southampton, UK, 2007.
  • Brauer, K. The Korteweg-de Vries equation: history, exact solutions, and graphical representation . University of Osnabruck, 2006.
  • Taha, T. R.; Ablowitz, M. J. J. Comput. Phys. 1984 , 55 , 231-253.
  • Momani, S. Math. Comput. Simulation 2005 , 70 , 110-118.
  • El-Wakil, S. A.; Abulwafa, E. M.; Zahran, M. A.; Mahmoud, A. A. Nonlinear Dyn. 2011 , 65 , 55-63.
  • Zhang, Y. Electron. J. Differ. Equ. 2014 , 2014 , 1-12.
  • Ganji, Z. Z.; Ganji, D. D.; Rostamiyan, Y. Appl. Math. Model. , 2009 , 33 , 3107-3113.
  • Machado, J. A. T.; Silva, M. F.; Barbosa, R. S.; Jesus, I. S.; Reis, C. M.; Marcos, M. G.; Galhano, A. F. Math. Prob. Eng. 2010 , 2010 , 1-34.
  • Sierociuk, D.; Dzielinski, A.; Sarwas, G.; Petras, I.; Podlubny, I.; Skovranek, T. Phil. Trans. R. Soc. A. 2012 , 371 , 1-10.
  • Podlubny, I. Fractional Differential Equations ; Academic Press: New York, NY, USA, 1999.
  • He, J. H; Wu, X. H. Comput. Math. Appl. 2007 , 54 , 881-894.
  • Adomian, G. J. Math. Anal. Appl. 1988 , 135 , 501-544.
  • Khalil, R.; Horani, M. A.; Yousef, A.; Sababheh, M. J. Comput. Appl. Math. 2014 , 264 , 65-70.
  • Abdaljawad, T. J. Comput. Appl. Math. 2014 , 279 , 57-66.
  • Anderson, D. R.; Ulness, D. J. J. Math. Phy. 2015 , 56 , 1-18.
  • Eslami, M. Appl. Math. Comput. 2016 , 285 , 141-148.
  • Karayer, H.; Demirhan, D.; Buyukkilic, F. Commun. Theor. Phys. . 2016 , 66 , 12-18.
  • Ortigueira, M. D.; Machado, J. A. T. J. Comput. Phys. 2015 , 293 , 4-13.
  • Iyiola, O. S.; Tasbozan, O,; Kurt, A.; Cenesiz, Y. Chaos Solitons Fractals 2017 , 94 , 1-7.
  • Eslami, M.; Rezazadeh, H. Calcolo 2016 , 1-11.
  • Feng, Z.; Meng, Q. Sci. China Ser. A 2007 , 50 , 412-422.
  • Shu, J. J. J. Phys. A Math. Gen. 1987 , 20 , 49-56.

Ayrıntılar

Birincil Dil İngilizce
Konular Fizik, Ortak Disiplinler
Bölüm Makaleler
Yazarlar

Hasibe Hale KARAYER>


Ahmet Doğan DEMİRHAN Bu kişi benim


Fevzi BÜYÜKKILIÇ Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2018
Yayınlandığı Sayı Yıl 2018, Cilt 42, Sayı 3

Kaynak Göster

Bibtex @araştırma makalesi { tbtkphysics490298, journal = {Turkish Journal of Physics}, issn = {1300-0101}, eissn = {1303-6122}, address = {}, publisher = {TÜBİTAK}, year = {2018}, volume = {42}, number = {3}, pages = {254 - 264}, title = {Analytical solutions of conformable time, space, and time–space fractional KdV equations}, key = {cite}, author = {Karayer, Hasibe Hale and Demirhan, Ahmet Doğan and Büyükkılıç, Fevzi} }
APA Karayer, H. H. , Demirhan, A. D. & Büyükkılıç, F. (2018). Analytical solutions of conformable time, space, and time–space fractional KdV equations . Turkish Journal of Physics , 42 (3) , 254-264 . Retrieved from https://dergipark.org.tr/tr/pub/tbtkphysics/issue/40696/490298
MLA Karayer, H. H. , Demirhan, A. D. , Büyükkılıç, F. "Analytical solutions of conformable time, space, and time–space fractional KdV equations" . Turkish Journal of Physics 42 (2018 ): 254-264 <https://dergipark.org.tr/tr/pub/tbtkphysics/issue/40696/490298>
Chicago Karayer, H. H. , Demirhan, A. D. , Büyükkılıç, F. "Analytical solutions of conformable time, space, and time–space fractional KdV equations". Turkish Journal of Physics 42 (2018 ): 254-264
RIS TY - JOUR T1 - Analytical solutions of conformable time, space, and time–space fractional KdV equations AU - Hasibe HaleKarayer, Ahmet DoğanDemirhan, FevziBüyükkılıç Y1 - 2018 PY - 2018 N1 - DO - T2 - Turkish Journal of Physics JF - Journal JO - JOR SP - 254 EP - 264 VL - 42 IS - 3 SN - 1300-0101-1303-6122 M3 - UR - Y2 - 2018 ER -
EndNote %0 Turkish Journal of Physics Analytical solutions of conformable time, space, and time–space fractional KdV equations %A Hasibe Hale Karayer , Ahmet Doğan Demirhan , Fevzi Büyükkılıç %T Analytical solutions of conformable time, space, and time–space fractional KdV equations %D 2018 %J Turkish Journal of Physics %P 1300-0101-1303-6122 %V 42 %N 3 %R %U
ISNAD Karayer, Hasibe Hale , Demirhan, Ahmet Doğan , Büyükkılıç, Fevzi . "Analytical solutions of conformable time, space, and time–space fractional KdV equations". Turkish Journal of Physics 42 / 3 (Haziran 2018): 254-264 .
AMA Karayer H. H. , Demirhan A. D. , Büyükkılıç F. Analytical solutions of conformable time, space, and time–space fractional KdV equations. Turkish Journal of Physics. 2018; 42(3): 254-264.
Vancouver Karayer H. H. , Demirhan A. D. , Büyükkılıç F. Analytical solutions of conformable time, space, and time–space fractional KdV equations. Turkish Journal of Physics. 2018; 42(3): 254-264.
IEEE H. H. Karayer , A. D. Demirhan ve F. Büyükkılıç , "Analytical solutions of conformable time, space, and time–space fractional KdV equations", Turkish Journal of Physics, c. 42, sayı. 3, ss. 254-264, Haz. 2018