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Holomorphic Solution for a Class of Korteweg-de Vries Equations Involving Fractional Order  ABSTRACT  |  FULL TEXT 

Year 2012, Volume: 41 Issue: 4, 477 - 485, 01.04.2012

References

  • Ahmad, B. and Sivasundaram, S. Existence of solutions for impulsive integral boundary value problems of fractional order, Nonlinear Analysis: Hybrid Systems 4 (1), 134–141, 2010.
  • Bonilla, B., Rivero, M., Rodr`ıguez-Germ`a, L. and Trujillo, J. J. Fractional differential equa- tions as alternative models to nonlinear differential equations, Applied Mathematics and Computation 187, 79–88, 2007.
  • Byers, P. and Himonas, A. Nonanalytic solutions of the KdV equation, Abstract and Applied Analysis 2004 (6), 453–460, 2004.
  • Ibrahim, R. W. On the existence for diffeo-integral inclusion of Sobolev-type of fractional order with applications, ANZIAM J. 52 (E), 1–21, 2010.
  • Ibrahim, R. W. On solutions for fractional diffusion problems, Elec. J. Diff. Eq. 2010 147, 1–11, 2010.
  • Ibrahim, R. W. and Darus, M. Subordination and superordination for analytic functions involving fractional integral operator, Complex Variables and Elliptic Equations 53, 1021– 1031, 2008.
  • Ibrahim, R. W. and Darus, M. Subordination and superordination for univalent solutions for fractional differential equations, J. Math. Anal. Appl. 345, 871–879, 2008.
  • Ibrahim, R. W. and Darus, M. Subordination and superordination for functions based on Dziok-Srivastava linear operator, Bull. Math. Anal. Appl. 2 (3), 15–26, 2010.
  • Jafari, H. and Firoozjaee, M. A. Homotopy analysis method for solving KDV equations, Surveys in Math. Appl. 5, 89–98, 2010. [10] Kaya, D. An application of the decomposition method for the KdVb equation, Appl. Math. Comput. 152, 279-ˆu288, 2004.
  • Liu, J. and Xua, M. Some exact solutions to Stefan problems with fractional differential equations, J. Math. Anal. Appl. 351 (2), 536–542, 2009.
  • Momani, S. M. and Ibrahim, R. W. On a fractional integral equation of periodic functions involving Weyl-Riesz operator in Banach algebras, J. Math. Anal. Appl. 339, 1210–1219, 2008.
  • Soliman, A. A. Collocation solution of the Korteweg-de Vries equation using septic splines, Int J Comput Math 81, 325–331, 2004. [14] Srivastava, H. M. and Owa, S. Univalent Functions, Fractional Calculus, and Their Appli- cations(Halsted Press, John Wiley and Sons, New York, Chichester, Brisban, and Toronto, 1989).
  • Wei, Z., Dong, W. and Che, J. Periodic boundary value problems for fractional differential equations involving Riemann-Liouville fractional derivative, Nonlinear Analysis: Theory, Methods and Applications 73 (10), 3232–3238, 2010.
  • Zaki, S. I. A quintic B-spline finite elements scheme for the KdVB equation, Comput. Math. Appl. Mech. Eng. 188, 121–134, 2000. [17] Jun-Xiao, Z. and Bo-Ling, G. Analytic solutions to forced KdV equation, Commun. Theor. Phys. (Beijing, China) 52, 279–283, 2009.

Holomorphic Solution for a Class of Korteweg-de Vries Equations Involving Fractional Order  ABSTRACT  |  FULL TEXT 

Year 2012, Volume: 41 Issue: 4, 477 - 485, 01.04.2012

References

  • Ahmad, B. and Sivasundaram, S. Existence of solutions for impulsive integral boundary value problems of fractional order, Nonlinear Analysis: Hybrid Systems 4 (1), 134–141, 2010.
  • Bonilla, B., Rivero, M., Rodr`ıguez-Germ`a, L. and Trujillo, J. J. Fractional differential equa- tions as alternative models to nonlinear differential equations, Applied Mathematics and Computation 187, 79–88, 2007.
  • Byers, P. and Himonas, A. Nonanalytic solutions of the KdV equation, Abstract and Applied Analysis 2004 (6), 453–460, 2004.
  • Ibrahim, R. W. On the existence for diffeo-integral inclusion of Sobolev-type of fractional order with applications, ANZIAM J. 52 (E), 1–21, 2010.
  • Ibrahim, R. W. On solutions for fractional diffusion problems, Elec. J. Diff. Eq. 2010 147, 1–11, 2010.
  • Ibrahim, R. W. and Darus, M. Subordination and superordination for analytic functions involving fractional integral operator, Complex Variables and Elliptic Equations 53, 1021– 1031, 2008.
  • Ibrahim, R. W. and Darus, M. Subordination and superordination for univalent solutions for fractional differential equations, J. Math. Anal. Appl. 345, 871–879, 2008.
  • Ibrahim, R. W. and Darus, M. Subordination and superordination for functions based on Dziok-Srivastava linear operator, Bull. Math. Anal. Appl. 2 (3), 15–26, 2010.
  • Jafari, H. and Firoozjaee, M. A. Homotopy analysis method for solving KDV equations, Surveys in Math. Appl. 5, 89–98, 2010. [10] Kaya, D. An application of the decomposition method for the KdVb equation, Appl. Math. Comput. 152, 279-ˆu288, 2004.
  • Liu, J. and Xua, M. Some exact solutions to Stefan problems with fractional differential equations, J. Math. Anal. Appl. 351 (2), 536–542, 2009.
  • Momani, S. M. and Ibrahim, R. W. On a fractional integral equation of periodic functions involving Weyl-Riesz operator in Banach algebras, J. Math. Anal. Appl. 339, 1210–1219, 2008.
  • Soliman, A. A. Collocation solution of the Korteweg-de Vries equation using septic splines, Int J Comput Math 81, 325–331, 2004. [14] Srivastava, H. M. and Owa, S. Univalent Functions, Fractional Calculus, and Their Appli- cations(Halsted Press, John Wiley and Sons, New York, Chichester, Brisban, and Toronto, 1989).
  • Wei, Z., Dong, W. and Che, J. Periodic boundary value problems for fractional differential equations involving Riemann-Liouville fractional derivative, Nonlinear Analysis: Theory, Methods and Applications 73 (10), 3232–3238, 2010.
  • Zaki, S. I. A quintic B-spline finite elements scheme for the KdVB equation, Comput. Math. Appl. Mech. Eng. 188, 121–134, 2000. [17] Jun-Xiao, Z. and Bo-Ling, G. Analytic solutions to forced KdV equation, Commun. Theor. Phys. (Beijing, China) 52, 279–283, 2009.
There are 14 citations in total.

Details

Primary Language Turkish
Journal Section Mathematics
Authors

Rabha W. Ibrahim This is me

Publication Date April 1, 2012
Published in Issue Year 2012 Volume: 41 Issue: 4

Cite

APA Ibrahim, R. W. (2012). Holomorphic Solution for a Class of Korteweg-de Vries Equations Involving Fractional Order  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics, 41(4), 477-485.
AMA Ibrahim RW. Holomorphic Solution for a Class of Korteweg-de Vries Equations Involving Fractional Order  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics. April 2012;41(4):477-485.
Chicago Ibrahim, Rabha W. “Holomorphic Solution for a Class of Korteweg-De Vries Equations Involving Fractional Order  ABSTRACT  |  FULL TEXT ”. Hacettepe Journal of Mathematics and Statistics 41, no. 4 (April 2012): 477-85.
EndNote Ibrahim RW (April 1, 2012) Holomorphic Solution for a Class of Korteweg-de Vries Equations Involving Fractional Order  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics 41 4 477–485.
IEEE R. W. Ibrahim, “Holomorphic Solution for a Class of Korteweg-de Vries Equations Involving Fractional Order  ABSTRACT  |  FULL TEXT ”, Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 4, pp. 477–485, 2012.
ISNAD Ibrahim, Rabha W. “Holomorphic Solution for a Class of Korteweg-De Vries Equations Involving Fractional Order  ABSTRACT  |  FULL TEXT ”. Hacettepe Journal of Mathematics and Statistics 41/4 (April 2012), 477-485.
JAMA Ibrahim RW. Holomorphic Solution for a Class of Korteweg-de Vries Equations Involving Fractional Order  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics. 2012;41:477–485.
MLA Ibrahim, Rabha W. “Holomorphic Solution for a Class of Korteweg-De Vries Equations Involving Fractional Order  ABSTRACT  |  FULL TEXT ”. Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 4, 2012, pp. 477-85.
Vancouver Ibrahim RW. Holomorphic Solution for a Class of Korteweg-de Vries Equations Involving Fractional Order  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics. 2012;41(4):477-85.