On the Lie Symmetry Analysis and Traveling Wave Solutions of Time Fractional Fifth-Order Modified Sawada-Kotera Equation

yasar, emrullah; YILDIRIM, Yakup

On the Lie Symmetry Analysis and Traveling Wave Solutions of Time Fractional Fifth-Order Modified Sawada-Kotera Equation

Emrullah YAŞAR, (Bursa Uludağ Üniversitesi)

Yakup YILDIRIM (Bursa Uludağ Üniversitesi)

Karaelmas Fen ve Mühendislik Dergisi

4 0

Yıl: 2018 Cilt: 8 Sayı: 2 Sayfa Aralığı: 411 - 416 Metin Dili: İngilizce İndeks Tarihi: 09-02-2020

On the Lie Symmetry Analysis and Traveling Wave Solutions of Time Fractional Fifth-Order Modified Sawada-Kotera Equation

Öz:

In this paper, we study Lie symmetry analysis of the time fractional fifth-order modified Sawada-Kotera equation (FMSK) withRiemann-Liouville derivative. Applying the adapted the Lie group theory to the equation under study, two dimensional Lie algebra isdeduced. Using the obtained nontrivial Lie point symmetry, it is shown that the equation can be converted into a nonlinear fifth orderordinary differential equation of fractional order in the meaning of the Erdelyi-Kober fractional derivative operator. In addition, weconstruct some exact traveling solutions for the FMSK using the sub-equation method.

Anahtar Kelime:

Zaman Kesirli Beşinci Mertebeden Modifiye Edilmiş Sawada-Kotera Denkleminin Lie Simetri Analizi ve İlerleyen Dalga Çözümleri

Öz:

Bu makalede Riemann-Liouville türevine sahip beşinci mertebeden zaman kesirli modifiye edilmiş Sawada-Kotera denkleminin Lie grup analizi araştırılmıştır. Lie grup teorisinin denkleme uygulanmasıyla iki boyutlu Lie cebri elde edilmiştir. Aşikar olmayan Lie simetrisinin kullanılmasıyla denklemin Erdelyi-Kober kesirli türev operatörü cinsinden beşinci mertebeden kesirli adi diferensiyel denkleme dönüştürülebileceği gösterilmiştir. Bunun yanında alt-denklem metodu kullanılarak denklemin bazı tam ilerleyen dalga çözümlerine ulaşılmıştır.

Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

Adem, AR., Khalique, CM. 2012. Symmetry reductions, exact solutions and conservation laws of a new coupled KdV system. Commun. Nonlinear Sci. Numer. Simul., 17: 3465-3475.
Adem, AR., Muatjetjeja, B. 2015. Conservation laws and exact solutions for a 2D Zakharov–Kuznetsov equation. App. Math. Lett., 48: 109-117.
Adem, AR., Lü, X. 2016. Travelling wave solutions of a two-dimensional generalized Sawada–Kotera equation. Nonlinear Dyn.,84(2): 915-922.
Adem, AR. 2016. The generalized (1+ 1)-dimensional and (2+ 1)-dimensional Ito equations: multiple exp-function algorithm and multiple wave solutions. Comput. Math. App.,71(6): 1248-1258.
Bekir, A., Güner, O., Çevikel, AC. 2013a. Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations. Abstr. Appl. Anal., Article ID 426462, 8 pages,
Bekir, A. Güner, Ö. 2013b. Exact solutions of nonlinear fractional differential equations by (G’/G)-expansion method. Chin. Phys. B, 22(11): 110-202.
Bekir, A., Güner, Ö. 2014. The-expansion method using modified Riemann--Liouville derivative for some space-time fractional differential equations. Ain Shams Eng. J., 5(3): 959-965.
Bekir, A., Güner, O., Ünsal, O. 2015. The First Integral Method for Exact Solutions of Nonlinear Fractional Differential Equations. J. Comput. Nonlinear Dyn., 10: 021020-1.
Gazizov, RK., Kasatkin, AA., Lukashcuk, SY. 2009. Symmetry properties of fractional diffusion equations. Phys. Scr., T136, 014016. Kilbas, AA., Srivastava, HM., Trujillo, JJ. 2006. Theory and applications of fractional differential equations, Elsevier, 132 pp.
Kiryakova, V. 1994. Generalised Fractional Calculus and Applications, Pitman Res. Notes in Math., 90 pp.
Konno, K. 1992. Conservation Laws of Modified Sawada-Kotera Equation in Complex Plane, J. Phys. Soc. Jpn., 61(1): 51-54.
Kudryashov, NA., Loguinova, NB. 2008. Extended simplest equation method for nonlinear differential equations. Appl. Math. Comput., 205: 396-402.
Liang, HG., Guo G X. 2012. An extension of the modified Sawada Kotera equation and conservation laws. Chin. Phys. B., 21(7): 070205.
Naz R., Naeem I., Khan, M. 2013. Conservation laws of some physical models via symbolic package GeM. Math. Prob. Eng.
Podlubny, I., 1999. Fractional differential equations , Academic Press, 41 pp.
Rui, W., Zhang, X. 2015. Invariant analysis and conservation laws for the time fractional foam drainage equation. Eur. Phys. J. Plus., 130(10): 1-7.
Sahadevan, R., Bakkyaraj, T. 2012. Invariant analysis of time fractional generalized Burgers and Korteweg--de Vries equations. J. Math. Anal. Appl., 393: 341-347.
Sahadevan, R., Bakkyaraj, T. 2014. Invariant subspace method and exact solutions of certain nonlinear time fractional partial differential equations. Fract. Calc. Appl. Anal., 18(1): 146-162.
Wang, GW., Xu, TZ. 2014. Invariant analysis and exact solutions of nonlinear time fractional Sharma--Tasso-Olver equation by Lie group analysis. Nonlinear Dynam., 76: 571-580.
Wang, GW., Kara AH., Fakhar, K. 2015. Symmetry analysis and conservation laws for the class of time-fractional nonlinear dispersive equation. Nonlinear Dynam., 1-7.
Yang, XJ., Baleanu, D., Srivastava, HM. 2015. Local Fractional Integral Transforms and Their Applications. Academic Press, 34 pp.
Zhang, S., Zhang HX. 2011. Fractional sub-equation method and its applications to nonlinear fractional PDEs, Phys. Lett. A, 375(7): 1069-1073.

APA	yasar e, YILDIRIM Y (2018). On the Lie Symmetry Analysis and Traveling Wave Solutions of Time Fractional Fifth-Order Modified Sawada-Kotera Equation. , 411 - 416.
Chicago	yasar emrullah,YILDIRIM Yakup On the Lie Symmetry Analysis and Traveling Wave Solutions of Time Fractional Fifth-Order Modified Sawada-Kotera Equation. (2018): 411 - 416.
MLA	yasar emrullah,YILDIRIM Yakup On the Lie Symmetry Analysis and Traveling Wave Solutions of Time Fractional Fifth-Order Modified Sawada-Kotera Equation. , 2018, ss.411 - 416.
AMA	yasar e,YILDIRIM Y On the Lie Symmetry Analysis and Traveling Wave Solutions of Time Fractional Fifth-Order Modified Sawada-Kotera Equation. . 2018; 411 - 416.
Vancouver	yasar e,YILDIRIM Y On the Lie Symmetry Analysis and Traveling Wave Solutions of Time Fractional Fifth-Order Modified Sawada-Kotera Equation. . 2018; 411 - 416.
IEEE	yasar e,YILDIRIM Y "On the Lie Symmetry Analysis and Traveling Wave Solutions of Time Fractional Fifth-Order Modified Sawada-Kotera Equation." , ss.411 - 416, 2018.
ISNAD	yasar, emrullah - YILDIRIM, Yakup. "On the Lie Symmetry Analysis and Traveling Wave Solutions of Time Fractional Fifth-Order Modified Sawada-Kotera Equation". (2018), 411-416.

APA	yasar e, YILDIRIM Y (2018). On the Lie Symmetry Analysis and Traveling Wave Solutions of Time Fractional Fifth-Order Modified Sawada-Kotera Equation. Karaelmas Fen ve Mühendislik Dergisi, 8(2), 411 - 416.
Chicago	yasar emrullah,YILDIRIM Yakup On the Lie Symmetry Analysis and Traveling Wave Solutions of Time Fractional Fifth-Order Modified Sawada-Kotera Equation. Karaelmas Fen ve Mühendislik Dergisi 8, no.2 (2018): 411 - 416.
MLA	yasar emrullah,YILDIRIM Yakup On the Lie Symmetry Analysis and Traveling Wave Solutions of Time Fractional Fifth-Order Modified Sawada-Kotera Equation. Karaelmas Fen ve Mühendislik Dergisi, vol.8, no.2, 2018, ss.411 - 416.
AMA	yasar e,YILDIRIM Y On the Lie Symmetry Analysis and Traveling Wave Solutions of Time Fractional Fifth-Order Modified Sawada-Kotera Equation. Karaelmas Fen ve Mühendislik Dergisi. 2018; 8(2): 411 - 416.
Vancouver	yasar e,YILDIRIM Y On the Lie Symmetry Analysis and Traveling Wave Solutions of Time Fractional Fifth-Order Modified Sawada-Kotera Equation. Karaelmas Fen ve Mühendislik Dergisi. 2018; 8(2): 411 - 416.
IEEE	yasar e,YILDIRIM Y "On the Lie Symmetry Analysis and Traveling Wave Solutions of Time Fractional Fifth-Order Modified Sawada-Kotera Equation." Karaelmas Fen ve Mühendislik Dergisi, 8, ss.411 - 416, 2018.
ISNAD	yasar, emrullah - YILDIRIM, Yakup. "On the Lie Symmetry Analysis and Traveling Wave Solutions of Time Fractional Fifth-Order Modified Sawada-Kotera Equation". Karaelmas Fen ve Mühendislik Dergisi 8/2 (2018), 411-416.