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YENİ BİR YARDIMCI DENKLEM KULLANARAK KESİRLİ RLW BURGES DENKLEMI IÇIN TAM ÇÖZÜM BULMA

Year 2013, Volume: 8 Issue: 1, 1 - 10, 01.02.2013

Abstract

Bu çalışmada kesirli lineer olmayan kısmi diferensiyel denklemlerin tam çözümlerinin oluşturulması için Riccati denkleminden farklı bir yardımcı denklem ile yeni bir metod kullanılmıştır. Bu metodun ana fikri, Riccati denkleminden farklı olarak yeni çözümlere sahip yeni bir yardımcı denklemden en iyi şekilde yararlanmaktır. Sonuç olarak, kesirli RLW Burgers denklemi için birçok yeni çözüm elde edilmiştir.

References

  • Miller, K.S. and Ross, B., (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York.
  • Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J., (2006). Theory and Applications of Fractional Differential Equations, Elsevier, San Diego.
  • Podlubny, I., (1999). Fractional Differential Equations, Academic Press, San Diego.
  • Jumarie, G., (2006). Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results, Comput. Math. Appl. 51(9-10), 1367–1376.
  • Jumarie, G., (2007). Fractional Hamilton-Jacobi equation for the optimal control of nonrandom fractional dynamics with fractional cost function, J. Appl. Math. Comput. 23(1-2), 215–228.
  • Jumarie, G., (2009). Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions, Appl. Math. Lett. 22(3), 378– 385.
  • Lu, B., (2012). The first integral method for some time fractional differential equations, J. Math. Anal. Appl. 395, 684–693.
  • Song, L.N. and Zhang, H.Q., (2009). Solving the fractional BBM- Burgers equation using the homotopy analysis method, Chaos Solitons Fractals 40,1616–1622.
  • Ganji, Z., Ganji, D., Ganji, A.D., and Rostamian, M., (2010). Analytical solution of time-fractional Navier–Stokes equation in polar coordinate by homotopy perturbation method, Numer. Methods Partial Differential Equations 26,117–124.
  • Gepreel, K.A., (2011). The homotopy perturbation method applied to the nonlinear fractional Kolmogorov–Petrovskii–Piskunov equations, Appl. Math. Lett. 24, 1428–1434.
  • Gupta, P.K. and Singh, M., (2011). Homotopy perturbation method for fractional Fornberg–Whitham equation, Comput. Math. Appl. 61, 50–254.
  • Jumarie, G., (2006). Lagrange characteristic method for solving a class of nonlinear partial differential equations of fractional order, Appl. Math. Lett. 19, 873–880.
  • Zhang, S. and Zhang, H.Q., (2011). Fractional sub-equation method and its applications to nonlinear fractional PDEs, Phys. Lett. A 375, 1069–1073.
  • Jumarie, G., (2006). Modified Riemann–Liouville derivative and fractional Taylor series of nondifferentiable functions further results, Comput. Math. Appl. 51, 1367–1376.
  • Feng, Z.S. and Roger, K., (2007). Traveling waves to a Burgers– Korteweg–de Vries-type equation with higher-order 10

FINDING EXACT SOLUTION BY USING A NEW AUXILIARY EQUATION FOR FRACTIONAL RLW BURGES EQUATION

Year 2013, Volume: 8 Issue: 1, 1 - 10, 01.02.2013

Abstract

In this study a new method with a different auxiliary equation from the Riccati equation is used for constructing exact solutions of fractional nonlinear partial differential equations. The main idea of this method is to take full advantage of a different auxiliary equation from the Riccati equation which has more new solutions. Finally, more new solutions have been obtained for the fractional RLW Burgers equation.

References

  • Miller, K.S. and Ross, B., (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York.
  • Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J., (2006). Theory and Applications of Fractional Differential Equations, Elsevier, San Diego.
  • Podlubny, I., (1999). Fractional Differential Equations, Academic Press, San Diego.
  • Jumarie, G., (2006). Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results, Comput. Math. Appl. 51(9-10), 1367–1376.
  • Jumarie, G., (2007). Fractional Hamilton-Jacobi equation for the optimal control of nonrandom fractional dynamics with fractional cost function, J. Appl. Math. Comput. 23(1-2), 215–228.
  • Jumarie, G., (2009). Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions, Appl. Math. Lett. 22(3), 378– 385.
  • Lu, B., (2012). The first integral method for some time fractional differential equations, J. Math. Anal. Appl. 395, 684–693.
  • Song, L.N. and Zhang, H.Q., (2009). Solving the fractional BBM- Burgers equation using the homotopy analysis method, Chaos Solitons Fractals 40,1616–1622.
  • Ganji, Z., Ganji, D., Ganji, A.D., and Rostamian, M., (2010). Analytical solution of time-fractional Navier–Stokes equation in polar coordinate by homotopy perturbation method, Numer. Methods Partial Differential Equations 26,117–124.
  • Gepreel, K.A., (2011). The homotopy perturbation method applied to the nonlinear fractional Kolmogorov–Petrovskii–Piskunov equations, Appl. Math. Lett. 24, 1428–1434.
  • Gupta, P.K. and Singh, M., (2011). Homotopy perturbation method for fractional Fornberg–Whitham equation, Comput. Math. Appl. 61, 50–254.
  • Jumarie, G., (2006). Lagrange characteristic method for solving a class of nonlinear partial differential equations of fractional order, Appl. Math. Lett. 19, 873–880.
  • Zhang, S. and Zhang, H.Q., (2011). Fractional sub-equation method and its applications to nonlinear fractional PDEs, Phys. Lett. A 375, 1069–1073.
  • Jumarie, G., (2006). Modified Riemann–Liouville derivative and fractional Taylor series of nondifferentiable functions further results, Comput. Math. Appl. 51, 1367–1376.
  • Feng, Z.S. and Roger, K., (2007). Traveling waves to a Burgers– Korteweg–de Vries-type equation with higher-order 10
There are 15 citations in total.

Details

Primary Language Turkish
Journal Section Physics
Authors

Hasan Bulut This is me

Publication Date February 1, 2013
Published in Issue Year 2013 Volume: 8 Issue: 1

Cite

APA Bulut, H. (2013). FINDING EXACT SOLUTION BY USING A NEW AUXILIARY EQUATION FOR FRACTIONAL RLW BURGES EQUATION. Physical Sciences, 8(1), 1-10. https://doi.org/10.12739/10.12739
AMA Bulut H. FINDING EXACT SOLUTION BY USING A NEW AUXILIARY EQUATION FOR FRACTIONAL RLW BURGES EQUATION. Physical Sciences. February 2013;8(1):1-10. doi:10.12739/10.12739
Chicago Bulut, Hasan. “FINDING EXACT SOLUTION BY USING A NEW AUXILIARY EQUATION FOR FRACTIONAL RLW BURGES EQUATION”. Physical Sciences 8, no. 1 (February 2013): 1-10. https://doi.org/10.12739/10.12739.
EndNote Bulut H (February 1, 2013) FINDING EXACT SOLUTION BY USING A NEW AUXILIARY EQUATION FOR FRACTIONAL RLW BURGES EQUATION. Physical Sciences 8 1 1–10.
IEEE H. Bulut, “FINDING EXACT SOLUTION BY USING A NEW AUXILIARY EQUATION FOR FRACTIONAL RLW BURGES EQUATION”, Physical Sciences, vol. 8, no. 1, pp. 1–10, 2013, doi: 10.12739/10.12739.
ISNAD Bulut, Hasan. “FINDING EXACT SOLUTION BY USING A NEW AUXILIARY EQUATION FOR FRACTIONAL RLW BURGES EQUATION”. Physical Sciences 8/1 (February 2013), 1-10. https://doi.org/10.12739/10.12739.
JAMA Bulut H. FINDING EXACT SOLUTION BY USING A NEW AUXILIARY EQUATION FOR FRACTIONAL RLW BURGES EQUATION. Physical Sciences. 2013;8:1–10.
MLA Bulut, Hasan. “FINDING EXACT SOLUTION BY USING A NEW AUXILIARY EQUATION FOR FRACTIONAL RLW BURGES EQUATION”. Physical Sciences, vol. 8, no. 1, 2013, pp. 1-10, doi:10.12739/10.12739.
Vancouver Bulut H. FINDING EXACT SOLUTION BY USING A NEW AUXILIARY EQUATION FOR FRACTIONAL RLW BURGES EQUATION. Physical Sciences. 2013;8(1):1-10.