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Dergiler / Turkish Journal of Mathematics and Computer Science / 2016 / Volume: 5

An Application of Improved Bernoulli Sub-Equation Function Method to The Nonlinear Time-Fractional Burgers Equation

Hasan Bulut
Gülnur Yel
Hacı Mehmet Başkonuş
Sayfa
—
Yayın Tarihi
2016-12-30
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Numerical simulation were depicted for di erent values of alpha.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this work, we study on the improved Bernoulli sub-equation function method.
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Temel Bulgular & Veri:We apply this method  to the nonlinear time-fractional Burgers equation.
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Sonuç & Katkı:Numerical simulation were depicted for di erent values of alpha.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Improved Bernoulli sub-equation function method · time-fractional Burgers equation · exponential function solution

Abstract

In this work, we study on the improved Bernoulli sub-equation function method. We apply this method  to the nonlinear time-fractional Burgers equation. We obtain new analytical solutions to this model for values of  n, m and M. Numerical simulation were depicted for di erent values of alpha.

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Bu Makaleye Atıf Yap

Bulut, H., Yel, G., Başkonuş, H. M. (2016). An Application of Improved Bernoulli Sub-Equation Function Method to The Nonlinear Time-Fractional Burgers Equation. Turkish Journal of Mathematics and Computer Science, Volume: 5. https://ajindex.com/articles/1324969

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Kaynakça (28)

  1. Atangana, A., On the new fractional derivative and application to nonlinear Fisher’s reaction-di ffusion equation, Applied Mathematics and Computation, 273(2016), 948-956. 2.1
  2. Atangana, A., Baleanu, D., New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model, Thermal Science, 1(2016), 763–769. 2.1, 2.2, 2.4
  3. Atangana, A., Koca, I., Chaos in a simple nonlinear system with Atangana- Baleanu derivatives with fractionalorder, Chaos, Solitons and Fractals, 1(2016), 447–454. 2.3
  4. Baskonus, H. M., Bulut, H., An e ective scheme for solving some nonlinear partial di erential equation arising in nonlinear physics, Open Physics, 13(2015), 280–289. 3
  5. Baskonus, H. M., Bulut, H., On the complex structures of Kundu-Eckhaus equation via improved Bernoulli sub-equation function method, Waves in Random and Complex Media, 25(2015), 720–728. 3
  6. Baskonus, H. M., Bulut, H., Exponential prototype structures for (2+1)-dimensional Boiti-Leon-Pempinelli systems in mathematical physics, Waves in Random and Complex Media, 26(2016), 201–208. 3
  7. Baskonus, H. M., Bulut, H., Regarding on the prototype solutions for the nonlinear fractional-order biological population model, AIP Conference Proceedings 1738(2016), 290004. 3
  8. Baskonus, H. M., Koc¸, D. A., Bulut, H., Dark and new travelling wave solutions to the nonlinear evolution equation, Optic-International Journal for Light and Electron Optics, 127(2016), 8043–8055. 3
  9. Bekir, A., Guner, O., Exact solutions of nonlinear fractional di erential equations by (G’/G)-expansion method, Chinese Physics B, 22(2013), 110202. 1, 4
  10. Burgers, J. M., A mathematical model illustrating the theory of turbulence, Advances in Applied Mechanics, 1(1948), 171–199. 1
  11. Doha, E. H., Bhrawy, A. H., Abdelkawy, M. A., Hafez, R. M., A Jacobi collocation approximation for nonlinear coupled viscous Burgers equation, Central European Journal of Physics, 12(2014), 111–122. 1
  12. Gepreel, K. A., Omran, S., Exact solutions for nonlinear partial fractional di erential equations, Chinese Physics B, 21(2012), 110204. 1
  13. Guo, S., Mei, L., Li, Y., Sun, Y., The improved fractional sub-equation method and its applications to the space-time fractional di erential equations in fluid mechanics, Physics Letters A, 376(2012), 407. 3
  14. Hammouch, Z., Mekkaoui, T., Travelling-wave solutions for some fractional partial di erential equation by means of generalized trigonometry functions, International Journal of Applied Mathematical Research, 1(2012), 206–212. 1
  15. Hammouch, Z., Mekkaoui, T., Chaos synchronization of a fractional nonautonomous system, Nonautonomous Dynamical Systems, 1(2014), 61–71. 1
  16. Harris, P. A., Garra, R., Analytic solution of nonlinear fractional Burgers-type equation by invariant subspace method, Nonlinear Studies, (2013), 471–481. 1
  17. He, J., Elagan, S. K., Li, Z. B., Geometrical explanation of the fractional complex transform and derivative Chain rule for fractional calculus, Physics Letters A, 376(2012) 257–259. 3
  18. Hussein, A., Selim, M. M., New soliton solutions for some important nonlinear partial di erential equations using a generalized Bernoulli method, International Journal of Mathematical Analysis and Applications, 1(2014), 1–8. 3
  19. Kurulay, M., The approximate and exact solutions of the space- and time- fractional Burgers equations, IJRRAS, 3(2010), 257. 1
  20. Momani, S., Non-perturbative analytical solutions of the space- and time- fractional Burgers equations, Chaos, Solitons and Fractals, 28(2006), 930–937. 1
  21. Moslem, W. M., Sabry, R., Zakharov-Kuznetsov-Burgers equation for Dust Ion acoustic waves, Chaos, Solitons and Fractals, 36(2008), 628. 1
  22. Rashidi, M. M., Erfani, E., New analytical method for solving Burgers and nonlinear heat transfer equations and comparison with HAM, Computer Physics Communications, 180(2009), 1539. 1
  23. Saad, M., Elagan, S. K., Hamed, Y. S., Sayed, M., Using a complex transformation to get an exact solutions for fractional generalized coupled MKDV and KDV equations, International Journal of Basic and Applied Sciences, 13(2013), 23–25. 3
  24. Sugimoto, N., Burgers equation with a fractional derivative: Hereditary e ects on nonlinear acoustic waves, Journal of Fluid Mechanics, 225(1991), 631. 1
  25. Yildirim, A., Mohyud-Din, S. T., Analytical approach to space- and time- fractional Burgers equations, Chinese Physics Letters, 27(2010), 9. 1
  26. Zhang, S., Hang, H. Q., Fractional sub-equation method and its applications to nonlinear fractional PDEs, Physics Letters A, 375(2011), 1069. 1
  27. Zhang, S., Zong, Q. A., Liu, D., Gao, Q., A Generalized exp-function method for fractional Riccati di erential equations, The Communications in Fractional Calculus, 1(2010), 48–51. 1
  28. Zhen, B. H., (G’/G)- expansion method for solving fractional partial di erential equations in the theory of mathematical physics, Communication Theory Physics, 58(2012), 623. 1