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

Yıl 2016, Cilt: 5 , 1 - 7, 30.12.2016

Öz

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.

Kaynakça

  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • Burgers, J. M., A mathematical model illustrating the theory of turbulence, Advances in Applied Mechanics, 1(1948), 171–199. 1
  • 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
  • Gepreel, K. A., Omran, S., Exact solutions for nonlinear partial fractional di erential equations, Chinese Physics B, 21(2012), 110204. 1
  • 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
  • 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
  • Hammouch, Z., Mekkaoui, T., Chaos synchronization of a fractional nonautonomous system, Nonautonomous Dynamical Systems, 1(2014), 61–71. 1
  • Harris, P. A., Garra, R., Analytic solution of nonlinear fractional Burgers-type equation by invariant subspace method, Nonlinear Studies, (2013), 471–481. 1
  • 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
  • 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
  • Kurulay, M., The approximate and exact solutions of the space- and time- fractional Burgers equations, IJRRAS, 3(2010), 257. 1
  • Momani, S., Non-perturbative analytical solutions of the space- and time- fractional Burgers equations, Chaos, Solitons and Fractals, 28(2006), 930–937. 1
  • Moslem, W. M., Sabry, R., Zakharov-Kuznetsov-Burgers equation for Dust Ion acoustic waves, Chaos, Solitons and Fractals, 36(2008), 628. 1
  • 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
  • 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
  • Sugimoto, N., Burgers equation with a fractional derivative: Hereditary e ects on nonlinear acoustic waves, Journal of Fluid Mechanics, 225(1991), 631. 1
  • Yildirim, A., Mohyud-Din, S. T., Analytical approach to space- and time- fractional Burgers equations, Chinese Physics Letters, 27(2010), 9. 1
  • Zhang, S., Hang, H. Q., Fractional sub-equation method and its applications to nonlinear fractional PDEs, Physics Letters A, 375(2011), 1069. 1
  • 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
  • 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
Yıl 2016, Cilt: 5 , 1 - 7, 30.12.2016

Öz

Kaynakça

  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • Burgers, J. M., A mathematical model illustrating the theory of turbulence, Advances in Applied Mechanics, 1(1948), 171–199. 1
  • 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
  • Gepreel, K. A., Omran, S., Exact solutions for nonlinear partial fractional di erential equations, Chinese Physics B, 21(2012), 110204. 1
  • 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
  • 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
  • Hammouch, Z., Mekkaoui, T., Chaos synchronization of a fractional nonautonomous system, Nonautonomous Dynamical Systems, 1(2014), 61–71. 1
  • Harris, P. A., Garra, R., Analytic solution of nonlinear fractional Burgers-type equation by invariant subspace method, Nonlinear Studies, (2013), 471–481. 1
  • 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
  • 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
  • Kurulay, M., The approximate and exact solutions of the space- and time- fractional Burgers equations, IJRRAS, 3(2010), 257. 1
  • Momani, S., Non-perturbative analytical solutions of the space- and time- fractional Burgers equations, Chaos, Solitons and Fractals, 28(2006), 930–937. 1
  • Moslem, W. M., Sabry, R., Zakharov-Kuznetsov-Burgers equation for Dust Ion acoustic waves, Chaos, Solitons and Fractals, 36(2008), 628. 1
  • 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
  • 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
  • Sugimoto, N., Burgers equation with a fractional derivative: Hereditary e ects on nonlinear acoustic waves, Journal of Fluid Mechanics, 225(1991), 631. 1
  • Yildirim, A., Mohyud-Din, S. T., Analytical approach to space- and time- fractional Burgers equations, Chinese Physics Letters, 27(2010), 9. 1
  • Zhang, S., Hang, H. Q., Fractional sub-equation method and its applications to nonlinear fractional PDEs, Physics Letters A, 375(2011), 1069. 1
  • 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
  • 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
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Makaleler
Yazarlar

Hasan Bulut

Gülnur Yel

Hacı Mehmet Başkonuş

Yayımlanma Tarihi 30 Aralık 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 5

Kaynak Göster

APA 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, 5, 1-7.
AMA Bulut H, Yel G, Başkonuş HM. An Application of Improved Bernoulli Sub-Equation Function Method to The Nonlinear Time-Fractional Burgers Equation. TJMCS. Aralık 2016;5:1-7.
Chicago Bulut, Hasan, Gülnur Yel, ve Hacı Mehmet Başkonuş. “An Application of Improved Bernoulli Sub-Equation Function Method to The Nonlinear Time-Fractional Burgers Equation”. Turkish Journal of Mathematics and Computer Science 5, Aralık (Aralık 2016): 1-7.
EndNote Bulut H, Yel G, Başkonuş HM (01 Aralık 2016) An Application of Improved Bernoulli Sub-Equation Function Method to The Nonlinear Time-Fractional Burgers Equation. Turkish Journal of Mathematics and Computer Science 5 1–7.
IEEE H. Bulut, G. Yel, ve H. M. Başkonuş, “An Application of Improved Bernoulli Sub-Equation Function Method to The Nonlinear Time-Fractional Burgers Equation”, TJMCS, c. 5, ss. 1–7, 2016.
ISNAD Bulut, Hasan vd. “An Application of Improved Bernoulli Sub-Equation Function Method to The Nonlinear Time-Fractional Burgers Equation”. Turkish Journal of Mathematics and Computer Science 5 (Aralık 2016), 1-7.
JAMA Bulut H, Yel G, Başkonuş HM. An Application of Improved Bernoulli Sub-Equation Function Method to The Nonlinear Time-Fractional Burgers Equation. TJMCS. 2016;5:1–7.
MLA Bulut, Hasan vd. “An Application of Improved Bernoulli Sub-Equation Function Method to The Nonlinear Time-Fractional Burgers Equation”. Turkish Journal of Mathematics and Computer Science, c. 5, 2016, ss. 1-7.
Vancouver Bulut H, Yel G, Başkonuş HM. An Application of Improved Bernoulli Sub-Equation Function Method to The Nonlinear Time-Fractional Burgers Equation. TJMCS. 2016;5:1-7.