BibTex RIS Kaynak Göster
Yıl 2018, Cilt: 67 Sayı: 1, 60 - 67, 01.02.2018
https://doi.org/10.1501/Commua1_0000000830

Öz

Kaynakça

  • Miller, K.S. and Ross, B., An introduction to the fractional calculus and fractional diğerential equations, Wiley, New York,1993.
  • Podlubny, I., Fractional Diğerential Equations, Academic Press, California, 1999.
  • Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J., Theory and Applictions of Fractional Dif- ferential Equations, Elsevier, Amsterdam, 2006.
  • Wang, X.L., Li, X.Z. and Zhang, J.L., The (G=G)-expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics, Physics Letters A (2008),372,417-423.
  • Zheng, B., (G=G)-expansion method for solving fractional partial diğerential equations in the theory of mathematical physics, Communications in Theoretical Physics (2012),58,623-630. [6] Gepreel,K.A. and Omran,S., Exact solutions for nonlinear partial fractional diğerential equa- tions, Chinese Physics B (2012),21, 110204.
  • Shang, N. and Zheng, B., Exact solutions for three fractional partial diğerential equations by the (G=G)method, International journal of Applied mathematics (2013),43, p114.
  • Lu, B., The …rst integral method for some time fractional diğerential equations, Journal of Mathematical Analysis and Applications (2012),395, 684-693.
  • Eslami, M., Vajargah, B.F. , Mirzazadeh, M. and Biswas, A., Application of …rst integral method to fractional partial diğerential equations, Indian Journal of Physics (2014),88, 177- 184.
  • Zhang, S., Zong, Q-A., Liu, D. and Gao, Q., A generalized exp-function method for fractional riccati diğerential equations, Communications in Fractional Calculus (2010),1, 48-51.
  • Bekir, A., Güner, Ö. and Çevikel, A.C.,Fractional complex transform and exp-function meth- ods for fractional diğerential equations, Abstract and Applied Analysis (2013),2013, 426462. [12] Zhang, B., Exp-function method for solving fractional partial diğerential equations, Scienti…c World Journal (2013),2013, 465723.
  • Liu, W. and Chen, K., The functional variable method for …nding exact solutions of some nonlinear time-fractional diğerentional equations, Pramana-Journal of Physics (2013),81, 377-384.
  • Zhang, S. and Zhang, H-Q., Fractional sub-equation method and its applications to nonlinear fractional PDEs, Physics Letters A (2011),375, 1069-1073.
  • Alzaidy, J.F., Fractional sub-equation method and its applications to the space-time fractional diğerential equations in mathematical physics, British Journal of Mathematics and Computer Science (2013),3, 153-163.
  • Zhang, S, Tong, J.L. and Wang, W., A Generalized -Expansion Method for the mKdV Equa- tion with Variable Coe¢ cients, Physics Letters A (2008),372, 2254-2257.
  • Zayed, E.M.E. and Gepreel, K.A., The (G=G)-expansion method for …nding traveling wave solutions of nonlinear partial diğerential equations in mathematical physics, Journal of math- ematical Physics (2009),50, 013502.
  • Jumarie, G., Fractional partial diğerential equations and modi…ed Riemann-Liouville deriv- ative new methods for solution, Journal of Applied Mathematics and Computation (2007),4, 31-48.
  • Jumarie, G., Table of some basic fractional calculus formulae derived from a modi…ed Riemann-Liouville derivative for nondiğerentiable functions, Applied Mathematics Letters (2009),22, 378-385.
  • Li, Z.B. and He, J., Fractional complex transform for fractional diğerential equations, Math- ematical & Computational Applications, (2010),15, 970-973.
  • Li, Z.B. and He, J., Application of the fractional complex transform to fractional diğerential equations, Nonlinear Science Letter A (2011),2, 121-126.
  • Heremant, W., Banerjeeg, P.P., Korpel, A., Assanto, G., Van Immerzeele, A. and Meerpoel, A., Exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method, Journal of Physics A:Mathematical and General (1986),19,607-628.
  • Liu, X., Tian, L. and Wu, Y., Application of (G=G)-expansion method to two nonlinear evolution equations, Applied Mathematics and Computation (2010),217, 1376-1384.
  • Tang, Y., Xu, W. and Shen, J., Solitary wave solutions to Gardner equation, Chinese journal of Engineering Mathematics (2007),24, 119-127.

Application of the (G0/G)-expansion method for some space-time fractional partial differential equations

Yıl 2018, Cilt: 67 Sayı: 1, 60 - 67, 01.02.2018
https://doi.org/10.1501/Commua1_0000000830

Öz

In this paper, the (G0/G)-expansion method is presented for finding the exact solutions of the space-time fractional traveling wave solutions for the Joseph-Egri (TRLW) equation and Gardner equation. The fractional derivatives are described by modified Riemann-Liouville sense. Many exact solutions are obtained by the hyperbolic functions, the trigonometric functions and the rational functions. This method is effcient and powerful in performing a solution to the fractional partial differential equations. Also, the method reduces the large amount of calculations

Kaynakça

  • Miller, K.S. and Ross, B., An introduction to the fractional calculus and fractional diğerential equations, Wiley, New York,1993.
  • Podlubny, I., Fractional Diğerential Equations, Academic Press, California, 1999.
  • Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J., Theory and Applictions of Fractional Dif- ferential Equations, Elsevier, Amsterdam, 2006.
  • Wang, X.L., Li, X.Z. and Zhang, J.L., The (G=G)-expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics, Physics Letters A (2008),372,417-423.
  • Zheng, B., (G=G)-expansion method for solving fractional partial diğerential equations in the theory of mathematical physics, Communications in Theoretical Physics (2012),58,623-630. [6] Gepreel,K.A. and Omran,S., Exact solutions for nonlinear partial fractional diğerential equa- tions, Chinese Physics B (2012),21, 110204.
  • Shang, N. and Zheng, B., Exact solutions for three fractional partial diğerential equations by the (G=G)method, International journal of Applied mathematics (2013),43, p114.
  • Lu, B., The …rst integral method for some time fractional diğerential equations, Journal of Mathematical Analysis and Applications (2012),395, 684-693.
  • Eslami, M., Vajargah, B.F. , Mirzazadeh, M. and Biswas, A., Application of …rst integral method to fractional partial diğerential equations, Indian Journal of Physics (2014),88, 177- 184.
  • Zhang, S., Zong, Q-A., Liu, D. and Gao, Q., A generalized exp-function method for fractional riccati diğerential equations, Communications in Fractional Calculus (2010),1, 48-51.
  • Bekir, A., Güner, Ö. and Çevikel, A.C.,Fractional complex transform and exp-function meth- ods for fractional diğerential equations, Abstract and Applied Analysis (2013),2013, 426462. [12] Zhang, B., Exp-function method for solving fractional partial diğerential equations, Scienti…c World Journal (2013),2013, 465723.
  • Liu, W. and Chen, K., The functional variable method for …nding exact solutions of some nonlinear time-fractional diğerentional equations, Pramana-Journal of Physics (2013),81, 377-384.
  • Zhang, S. and Zhang, H-Q., Fractional sub-equation method and its applications to nonlinear fractional PDEs, Physics Letters A (2011),375, 1069-1073.
  • Alzaidy, J.F., Fractional sub-equation method and its applications to the space-time fractional diğerential equations in mathematical physics, British Journal of Mathematics and Computer Science (2013),3, 153-163.
  • Zhang, S, Tong, J.L. and Wang, W., A Generalized -Expansion Method for the mKdV Equa- tion with Variable Coe¢ cients, Physics Letters A (2008),372, 2254-2257.
  • Zayed, E.M.E. and Gepreel, K.A., The (G=G)-expansion method for …nding traveling wave solutions of nonlinear partial diğerential equations in mathematical physics, Journal of math- ematical Physics (2009),50, 013502.
  • Jumarie, G., Fractional partial diğerential equations and modi…ed Riemann-Liouville deriv- ative new methods for solution, Journal of Applied Mathematics and Computation (2007),4, 31-48.
  • Jumarie, G., Table of some basic fractional calculus formulae derived from a modi…ed Riemann-Liouville derivative for nondiğerentiable functions, Applied Mathematics Letters (2009),22, 378-385.
  • Li, Z.B. and He, J., Fractional complex transform for fractional diğerential equations, Math- ematical & Computational Applications, (2010),15, 970-973.
  • Li, Z.B. and He, J., Application of the fractional complex transform to fractional diğerential equations, Nonlinear Science Letter A (2011),2, 121-126.
  • Heremant, W., Banerjeeg, P.P., Korpel, A., Assanto, G., Van Immerzeele, A. and Meerpoel, A., Exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method, Journal of Physics A:Mathematical and General (1986),19,607-628.
  • Liu, X., Tian, L. and Wu, Y., Application of (G=G)-expansion method to two nonlinear evolution equations, Applied Mathematics and Computation (2010),217, 1376-1384.
  • Tang, Y., Xu, W. and Shen, J., Solitary wave solutions to Gardner equation, Chinese journal of Engineering Mathematics (2007),24, 119-127.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Aylin Mine Bayrak Bu kişi benim

Yayımlanma Tarihi 1 Şubat 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 67 Sayı: 1

Kaynak Göster

APA Bayrak, A. M. (2018). Application of the (G0/G)-expansion method for some space-time fractional partial differential equations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67(1), 60-67. https://doi.org/10.1501/Commua1_0000000830
AMA Bayrak AM. Application of the (G0/G)-expansion method for some space-time fractional partial differential equations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Şubat 2018;67(1):60-67. doi:10.1501/Commua1_0000000830
Chicago Bayrak, Aylin Mine. “Application of the (G0/G)-Expansion Method for Some Space-Time Fractional Partial Differential Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67, sy. 1 (Şubat 2018): 60-67. https://doi.org/10.1501/Commua1_0000000830.
EndNote Bayrak AM (01 Şubat 2018) Application of the (G0/G)-expansion method for some space-time fractional partial differential equations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67 1 60–67.
IEEE A. M. Bayrak, “Application of the (G0/G)-expansion method for some space-time fractional partial differential equations”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 67, sy. 1, ss. 60–67, 2018, doi: 10.1501/Commua1_0000000830.
ISNAD Bayrak, Aylin Mine. “Application of the (G0/G)-Expansion Method for Some Space-Time Fractional Partial Differential Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67/1 (Şubat 2018), 60-67. https://doi.org/10.1501/Commua1_0000000830.
JAMA Bayrak AM. Application of the (G0/G)-expansion method for some space-time fractional partial differential equations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67:60–67.
MLA Bayrak, Aylin Mine. “Application of the (G0/G)-Expansion Method for Some Space-Time Fractional Partial Differential Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 67, sy. 1, 2018, ss. 60-67, doi:10.1501/Commua1_0000000830.
Vancouver Bayrak AM. Application of the (G0/G)-expansion method for some space-time fractional partial differential equations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67(1):60-7.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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