1887
Volume 2013, Issue 1
  • E-ISSN: 2223-506X

ملخص

This paper shows the combination of an efficient transformation and Exp-function method, to construct generalized solitary wave solutions of the nonlinear Burger's equations of fractional-order. Computational work and subsequent numerical results re-confirm the efficiency of the proposed algorithm. It is observed that the suggested scheme is highly reliable and may be extended to other nonlinear differential equations of fractional order.

Loading

جارٍ تحميل قياسات المقالة...

/content/journals/10.5339/connect.2013.19
٢٠١٣-٠٧-٠١
٢٠٢٤-٠٧-٠٣
Loading full text...

Full text loading...

/deliver/fulltext/connect/2013/1/connect.2013.19.html?itemId=/content/journals/10.5339/connect.2013.19&mimeType=html&fmt=ahah

References

  1. Hilfer R, ed. Applications of Fractional Calculus in Physics. World Scientific 2000;
    [Google الباحث العلمي]
  2. Kilbas AA, Srivastava HM, Trujillo JJ. Theory and Applications of Fractional Differential Equations. Amsterdam, The Netherlands: Elsevier 2006:.204
    [Google الباحث العلمي]
  3. Miller KS, Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations. New York, NY, USA: Wiley-Interscience, John Wiley & Sons 1993;
    [Google الباحث العلمي]
  4. Podlubny I. Fractional Differential Equations. Mathematics in Science and Engineering. San Diego, California, USA: Academic Press 1999:.198
    [Google الباحث العلمي]
  5. Shawagfeh NT. Analytical approximate solutions for nonlinear fractional differential equations. Appl Math Comput. 2002; 131:2-3:517529
    [Google الباحث العلمي]
  6. Saha Ray S, Bera RK. An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method. Appl Math Comput. 2005; 167:1:561571
    [Google الباحث العلمي]
  7. He JH. Some applications of nonlinear fractional differential equations and their approximations. Bull Sci Tech. 1999; 15:2:8690
    [Google الباحث العلمي]
  8. Yıldırım A, Mohyud-Din ST, Sarıaydın S. Numerical comparison for the solutions of anharmonic vibration of fractionally damped nano-sized oscillator. J King Saud University Sci. 2011; 23:2:205209
    [Google الباحث العلمي]
  9. He J-H, Wu X-H. Exp-function method for nonlinear wave equations. Chaos Soliton Fract. 2006; 30:3:700708
    [Google الباحث العلمي]
  10. HE J-H. An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering. Int J Mod Phys B. 2008; 22:21:34873578
    [Google الباحث العلمي]
  11. He J-H, Abdou MA. New periodic solutions for nonlinear evolution equations using Exp-function method. Chaos Soliton Fract. 2007; 34:5:14211429
    [Google الباحث العلمي]
  12. Mohyud-Din ST, Noor MA, Waheed A. Exp-function method for generalized traveling solutions of good Boussinesq equations. J Appl Math Comput. 2009; 30:1-2:439445
    [Google الباحث العلمي]
  13. Mohyud-Din ST, Noor MA, Noor KI. Some Relatively New Techniques for Nonlinear Problems. Math Probl Eng. 2009; 2009::126
    [Google الباحث العلمي]
  14. Noor MA, Mohyud-Din ST, Waheed A. Exp-function method for solving Kuramoto-Sivashinsky and Boussinesq equations. J Appl Math Comp. 2009; 29:1-2:113
    [Google الباحث العلمي]
  15. Noor MA, Mohyud-Din ST, Waheed A. Exp-function Method for Generalized Traveling Solutions of Master Partial Differential Equation. Acta Applicandae Mathematicae. 2008; 104:2:131137
    [Google الباحث العلمي]
  16. Öziş T, Köroğlu C. A novel approach for solving the Fisher equation using Exp-function method. Phys Lett A. 2008; 372:21:38363840
    [Google الباحث العلمي]
  17. (Benn)Wu X-H, He J-H. EXP-function method and its application to nonlinear equations. Chaos Soliton Fract. 2008; 38:3:903910
    [Google الباحث العلمي]
  18. Wu X-H (Benn), He J-H. Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method. Comput Math Appl. 2007; 54:7-8:966986
    [Google الباحث العلمي]
  19. Yusufoğlu E. New solitonary solutions for the MBBM equations using Exp-function method. Phys Lett A. 2008; 372:4:442446
    [Google الباحث العلمي]
  20. Zhang S. Application of Exp-function method to high-dimensional nonlinear evolution equation. Chaos Soliton Fract. 2008; 38:1:270276
    [Google الباحث العلمي]
  21. Zhu SD. Exp-function Method for the Hybrid-Lattice System. Int J Nonlin Sci Num. 2007; 8:3
    [Google الباحث العلمي]
  22. Zhu S-D. Exp-function Method for the Discrete mKdV Lattice. Int J Nonlin Sci Num. 2007; 8:3
    [Google الباحث العلمي]
  23. Kudryashov NA. Exact soliton solutions of the generalized evolution equation of wave dynamics. J Appl Math Mech. 1988; 52:3:361365
    [Google الباحث العلمي]
  24. Momani S. An explicit and numerical solutions of the fractional KdV equation. Math Comput Simulat. 2005; 70:2:110118
    [Google الباحث العلمي]
  25. He JH, Li ZB. Fractional complex transform for fractional differential equations. Math Comput Appl. 2010; 15:5:970973
    [Google الباحث العلمي]
  26. Li Z-B. An Extended Fractional Complex Transform. Int J Non Sci Num Simulat. 2010; 11:Supplement
    [Google الباحث العلمي]
  27. He J-H, Li Z-B. Converting fractional differential equations into partial differential equations. Therm Sci. 2012; 16:2:331334
    [Google الباحث العلمي]
  28. Jumarie G. Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results. Comput Math Appl. 2006; 51:9-10:13671376
    [Google الباحث العلمي]
  29. Momani S. Non-perturbative analytical solutions of the space- and time-fractional Burgers equations. Chaos Soliton Fract. 2006; 28:4:930937
    [Google الباحث العلمي]
  30. Wang Q. Homotopy perturbation method for fractional KdV-Burgers equation. Chaos Soliton Fract. 2008; 35:5:843850
    [Google الباحث العلمي]
  31. Ebaid A. An improvement on the Exp-function method when balancing the highest order linear and nonlinear terms. J Math Anal Appl. 2012; 392:1:15
    [Google الباحث العلمي]
  32. Ma WX. Complexiton solutions to the Korteweg-de Vries equation. Phys Lett A. 2002; 301:1-2:3544
    [Google الباحث العلمي]
  33. Ma WX, Fuchssteiner B. Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation. Int J Nonlin Mech. 1996; 31:3:329338
    [Google الباحث العلمي]
  34. Ma W-X, You Y. Solving the Korteweg-de-Vries equation by its bilinear form: Wronskian solutions. Tran American Math Soc. 2005; 357:05:17531779
    [Google الباحث العلمي]
  35. Ma WX, You Y. Rational solutions of the Toda lattice equation in Casoratian form. Chaos Soliton Fract. 2004; 22:2:395406
    [Google الباحث العلمي]
  36. Ma W-X, Wu H, He J. Partial differential equations possessing Frobenius integrable decompositions. Phys Lett A. 2007; 364:1:2932
    [Google الباحث العلمي]
  37. Mohyud-Din ST. Solution of nonlinear differential equations by Exp-function method. World Appl Sci J. 2009; 7::116147
    [Google الباحث العلمي]
  38. Abdou MA, Soliman AA, El-Basyony ST. New application of Exp-function method for improved Boussinesq equation. Phys Lett A. 2007; 369:5-6:469475
    [Google الباحث العلمي]
  39. Zheng B. G′/G- Expansion Method for Solving Fractional Partial Differential Equations in the Theory of Mathematical Physics. Commun Theor Phys. 2012; 58:5:623630
    [Google الباحث العلمي]
/content/journals/10.5339/connect.2013.19
Loading
/content/journals/10.5339/connect.2013.19
Loading

جارٍ تحميل البيانات والوسائط...

  • نوع المستند: Research Article
الموضوعات الرئيسية Burger's equationsexp-function methodfractional calculus and modified Riemann-Liouville derivative
هذه الخانة مطلوبة
يُرجى إدخال عنوان بريد إلكتروني صالح
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error