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

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

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  • 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.