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New Wave Solutions of Time Fractional Kadomtsev-Petviashvili Equation Arising In the Evolution of Nonlinear Long Waves of Small Amplitude

Yıl 2019, , 807 - 815, 31.08.2019
https://doi.org/10.18185/erzifbed.488506

Öz

The main aim of this paper is to obtain the
travelling wave solutions of fractional Kadomtsev- Petviashvili(KP) Equation
where the derivative is in conformable sense. For this aim the sub equation
method is used with computer software called Mathematica. Then, solutions are
investigated through the graphical representation for different cases of

Kaynakça

  • [1] Khalil, R., Al Horani, M., Yousef, A., Sababheh, M., (2014), A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264, 65-70.
  • [2] Abdeljawad, T., (2015), On conformable fractional calculus. Journal of computational and Applied Mathematics, 279, 57-66.
  • [3] Kurt, A., Tasbozan, O., (2015)., Approximate Analytical Solution of the Time Fractional Whitham-Broer-Kaup Equation Using the Homotopy Analysis Method. International Jour-nal of Pure and Applied Mathematics, 98(4), 503-510.
  • [4] Alquran, M., (2014), Analytical solutions of fractional foam drainage equation by residual power series method. Mathematical sciences, 8(4), 153-160.
  • [5] El-Ajou, A., Arqub, O. A., Zhour, Z. A., Momani, S., (2013), New results on fractional power series: theories and applications. Entropy, 15(12), 5305-5323.
  • [6] Jaradat, H. M., Al-Shara, S., Khan, Q. J., Alquran, M., Al-Khaled, K., (2016), Analytical solution of time-fractional Drinfeld-Sokolov-Wilson system using residual power series method. IAENG Int. J. Appl. Math, 46(1), 64-70.
  • [7] Kumar, A., Kumar, S., Singh, M., (2016), Residual power series method for fractional Sharma-Tasso-Olever equation. Communications in Numerical Analysis, 2016(1), 1-10.
  • [8] Senol, M., Kasmaei, H. D., (2017), On the Comparison of Perturbation-Iteration Algorithm and Residual Power Series Method to Solve Fractional Zakharov-Kuznetsov Equation. arXiv preprint arXiv:1708.07970.
  • [9] Li, Z., (2014), Heteroclinic Breather-Wave for the Coupled Schrdinger Boussinesq Equation. Applied Mathematical Sciences, 8(120), 5995-6000.
  • [10] Chowdhury, A. R., Rao, N. N., (1998), Painlve Analysis and Backlund Transformations for Coupled Generalized Schrdinger Boussinesq System. Chaos, Solitons and Fractals, 9(10), 1747-1753.
  • [11] Huang, X., (2013), The investigation of solutions to the coupled Schrödinger-Boussinesq equations. Abstract and Applied Analysis (Vol. 2013). Hindawi.
  • [12] Zayed, E. M. E., Alurr, K. A. E., (2014), On solving the nonlinear Schrödinger-Boussinesq equation and the hyperbolic Schrödinger equation by using the expansion method. International Journal of Physical Sciences, 9(19), 415-429.
  • [13] Khater, M. M., Kumar, D., (2017), Implementation of three reliable methods for nding the exact solutions of (2+1) dimensional generalized fractional evolution equations. Optical and Quantum Electronics, 49(12), 427.
  • [14] Kaplan, M., Bekir, A., (2016), A novel analytical method for time-fractional differential equations. Optik-International Journal for Light and Electron Optics, 127(20), 8209-8214.
  • [15] Cenesiz, Y., A. Kurt., (2016), New fractional complex transform for conformable fractional partial differential equations." Journal of Applied Mathematics, Statistics and Informatics, 12, 41-47.
  • [16] Korkmaz, A., (2017), Exact solutions to (3+1) conformable time fractional Jimbo-Miwa-Zakharov-Kuznetsov and modified Zakharov-Kuznetsov equations. Communications in Theoretical Physics, 67(5), 479.
  • [17] 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(8), 278.
  • [18] Cenesiz, Y., Baleanu, D., Kurt, A., Tasbozan, O., (2017), New exact solutions of Burgers type equations with conformable derivative. Waves in Random and Complex Media, 27(1), 103-116.
  • [19] Kurt, A., Tasbozan, O., Baleanu, D., (2017), New solutions for conformable fractional Nizhnik-Novikov-Veselov system via -expansion method and homotopy analysis methods. Optical and Quantum Electronics, 49(10), 333.
  • [20] Hosseini, K., Mayeli, P., Ansari, R., (2017), Bright and singular soliton solutions of the conformable time-fractional Klein{Gordon equations with different nonlinearities. Waves in Random and Complex Media, 1-9.
  • [21] Rezazadeh, H., Manafian, J., Khodadad, F. S., Nazari, F., (2018), Traveling wave solutions for density-dependent conformable fractional diffusion-reaction equation by the first integral method and the improved -expansion method. Optical and Quantum Electronics, 50(3), 121.
  • [22] Eslami, M., Khodadad, F. S., Nazari, F., Rezazadeh, H., (2017), The first integral method applied to the Bogoyavlenskii equations by means of conformable fractional derivative. Optical and Quantum Electronics, 49(12), 391.
  • [23] Khodadad, F. S., Nazari, F., Eslami, M., Rezazadeh, H., (2017), Soliton solutions of the conformable fractional Zakharov-Kuznetsov equation with dual-power law nonlinearity. Optical and Quantum Electronics, 49(11), 384.
  • [24] Eslami, M., Rezazadeh, H., Rezazadeh, M., Mosavi, S. S., (2017), Exact solutions to the space-time fractional Schrdinger-Hirota equation and the space-time modified KDV-Zakharov Kuznetsov equation. Optical and Quantum Electronics, 49(8), 279.
  • [25] Eslami, M., Rezazadeh, H., (2016), The first integral method for Wu-Zhang system with conformable time-fractional derivative. Calcolo, 53(3), 475-485.
  • [26] Aminikhah, H., Sheikhani, A. R., Rezazadeh, H., (2016), Sub-equation method for the fractional regularized long-wave equations with conformable fractional derivatives. Scientia Iranica. Transaction B, Mechanical Engineering, 23(3), 1048.
  • [27] Zhang, Sheng, and Hong-Qing Zhang., (2011), Fractional sub-equation method and its applications to nonlinear fractional PDEs", Physics Letters A, 375.7(2011), 1069-1073.
  • [28] Abdeljawad T., (2015), On conformable fractional calulus, J. Comput. Appl. Math., 279, 57-66.
  • [29] Malfiet, W, (1992), Solitary wave solutions of nonlinear wave equations, American Journal of Physics 60, 650-654.

Küçük Genlikli Lineer Olmayan Uzun Dalgaların Gelişiminde Türeyen Zaman Kesirli Kadomtsev-Petviashvili Denkleminin Yeni Dalga Çözümleri

Yıl 2019, , 807 - 815, 31.08.2019
https://doi.org/10.18185/erzifbed.488506

Öz


 Bu makalenin asıl amacı, türevleri conformable
cinsinden olan kesirli Kadomtsev-Petviashvili (KP) denkleminin dalga
çözümlerini bulmaktır. Bu amaç için alt denklem metodu, Mathematica bilgisayar
programı ile birlikte kullanılmıştır. Daha sonra elde edilen çözümlerin
’ nın değişik değerleri için grafiksel gösterimleri
verilmiştir.



Kaynakça

  • [1] Khalil, R., Al Horani, M., Yousef, A., Sababheh, M., (2014), A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264, 65-70.
  • [2] Abdeljawad, T., (2015), On conformable fractional calculus. Journal of computational and Applied Mathematics, 279, 57-66.
  • [3] Kurt, A., Tasbozan, O., (2015)., Approximate Analytical Solution of the Time Fractional Whitham-Broer-Kaup Equation Using the Homotopy Analysis Method. International Jour-nal of Pure and Applied Mathematics, 98(4), 503-510.
  • [4] Alquran, M., (2014), Analytical solutions of fractional foam drainage equation by residual power series method. Mathematical sciences, 8(4), 153-160.
  • [5] El-Ajou, A., Arqub, O. A., Zhour, Z. A., Momani, S., (2013), New results on fractional power series: theories and applications. Entropy, 15(12), 5305-5323.
  • [6] Jaradat, H. M., Al-Shara, S., Khan, Q. J., Alquran, M., Al-Khaled, K., (2016), Analytical solution of time-fractional Drinfeld-Sokolov-Wilson system using residual power series method. IAENG Int. J. Appl. Math, 46(1), 64-70.
  • [7] Kumar, A., Kumar, S., Singh, M., (2016), Residual power series method for fractional Sharma-Tasso-Olever equation. Communications in Numerical Analysis, 2016(1), 1-10.
  • [8] Senol, M., Kasmaei, H. D., (2017), On the Comparison of Perturbation-Iteration Algorithm and Residual Power Series Method to Solve Fractional Zakharov-Kuznetsov Equation. arXiv preprint arXiv:1708.07970.
  • [9] Li, Z., (2014), Heteroclinic Breather-Wave for the Coupled Schrdinger Boussinesq Equation. Applied Mathematical Sciences, 8(120), 5995-6000.
  • [10] Chowdhury, A. R., Rao, N. N., (1998), Painlve Analysis and Backlund Transformations for Coupled Generalized Schrdinger Boussinesq System. Chaos, Solitons and Fractals, 9(10), 1747-1753.
  • [11] Huang, X., (2013), The investigation of solutions to the coupled Schrödinger-Boussinesq equations. Abstract and Applied Analysis (Vol. 2013). Hindawi.
  • [12] Zayed, E. M. E., Alurr, K. A. E., (2014), On solving the nonlinear Schrödinger-Boussinesq equation and the hyperbolic Schrödinger equation by using the expansion method. International Journal of Physical Sciences, 9(19), 415-429.
  • [13] Khater, M. M., Kumar, D., (2017), Implementation of three reliable methods for nding the exact solutions of (2+1) dimensional generalized fractional evolution equations. Optical and Quantum Electronics, 49(12), 427.
  • [14] Kaplan, M., Bekir, A., (2016), A novel analytical method for time-fractional differential equations. Optik-International Journal for Light and Electron Optics, 127(20), 8209-8214.
  • [15] Cenesiz, Y., A. Kurt., (2016), New fractional complex transform for conformable fractional partial differential equations." Journal of Applied Mathematics, Statistics and Informatics, 12, 41-47.
  • [16] Korkmaz, A., (2017), Exact solutions to (3+1) conformable time fractional Jimbo-Miwa-Zakharov-Kuznetsov and modified Zakharov-Kuznetsov equations. Communications in Theoretical Physics, 67(5), 479.
  • [17] 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(8), 278.
  • [18] Cenesiz, Y., Baleanu, D., Kurt, A., Tasbozan, O., (2017), New exact solutions of Burgers type equations with conformable derivative. Waves in Random and Complex Media, 27(1), 103-116.
  • [19] Kurt, A., Tasbozan, O., Baleanu, D., (2017), New solutions for conformable fractional Nizhnik-Novikov-Veselov system via -expansion method and homotopy analysis methods. Optical and Quantum Electronics, 49(10), 333.
  • [20] Hosseini, K., Mayeli, P., Ansari, R., (2017), Bright and singular soliton solutions of the conformable time-fractional Klein{Gordon equations with different nonlinearities. Waves in Random and Complex Media, 1-9.
  • [21] Rezazadeh, H., Manafian, J., Khodadad, F. S., Nazari, F., (2018), Traveling wave solutions for density-dependent conformable fractional diffusion-reaction equation by the first integral method and the improved -expansion method. Optical and Quantum Electronics, 50(3), 121.
  • [22] Eslami, M., Khodadad, F. S., Nazari, F., Rezazadeh, H., (2017), The first integral method applied to the Bogoyavlenskii equations by means of conformable fractional derivative. Optical and Quantum Electronics, 49(12), 391.
  • [23] Khodadad, F. S., Nazari, F., Eslami, M., Rezazadeh, H., (2017), Soliton solutions of the conformable fractional Zakharov-Kuznetsov equation with dual-power law nonlinearity. Optical and Quantum Electronics, 49(11), 384.
  • [24] Eslami, M., Rezazadeh, H., Rezazadeh, M., Mosavi, S. S., (2017), Exact solutions to the space-time fractional Schrdinger-Hirota equation and the space-time modified KDV-Zakharov Kuznetsov equation. Optical and Quantum Electronics, 49(8), 279.
  • [25] Eslami, M., Rezazadeh, H., (2016), The first integral method for Wu-Zhang system with conformable time-fractional derivative. Calcolo, 53(3), 475-485.
  • [26] Aminikhah, H., Sheikhani, A. R., Rezazadeh, H., (2016), Sub-equation method for the fractional regularized long-wave equations with conformable fractional derivatives. Scientia Iranica. Transaction B, Mechanical Engineering, 23(3), 1048.
  • [27] Zhang, Sheng, and Hong-Qing Zhang., (2011), Fractional sub-equation method and its applications to nonlinear fractional PDEs", Physics Letters A, 375.7(2011), 1069-1073.
  • [28] Abdeljawad T., (2015), On conformable fractional calulus, J. Comput. Appl. Math., 279, 57-66.
  • [29] Malfiet, W, (1992), Solitary wave solutions of nonlinear wave equations, American Journal of Physics 60, 650-654.
Toplam 29 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

HÜLYA Durur 0000-0002-9297-6873

ORKUN Taşbozan 0000-0001-5003-6341

ALİ Kurt Bu kişi benim 0000-0002-0617-6037

MEHMET Şenol 0000-0001-8110-7739

Yayımlanma Tarihi 31 Ağustos 2019
Yayımlandığı Sayı Yıl 2019

Kaynak Göster

APA Durur, H., Taşbozan, O., Kurt, A., Şenol, M. (2019). New Wave Solutions of Time Fractional Kadomtsev-Petviashvili Equation Arising In the Evolution of Nonlinear Long Waves of Small Amplitude. Erzincan University Journal of Science and Technology, 12(2), 807-815. https://doi.org/10.18185/erzifbed.488506

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Traveling Wave Solution of Vakhnenko-Parkes Equation
Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi
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https://doi.org/10.18185/erzifbed.676516