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

Abstract

-

Keywords

• -

References

1. 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.
2. 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.
3. Byers, P. and Himonas, A. Nonanalytic solutions of the KdV equation, Abstract and Applied Analysis 2004 (6), 453–460, 2004.
4. 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.
5. Ibrahim, R. W. On solutions for fractional diffusion problems, Elec. J. Diff. Eq. 2010 147, 1–11, 2010.
6. 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.
7. Ibrahim, R. W. and Darus, M. Subordination and superordination for univalent solutions for fractional differential equations, J. Math. Anal. Appl. 345, 871–879, 2008.
8. 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.

9. 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.
10. Liu, J. and Xua, M. Some exact solutions to Stefan problems with fractional differential equations, J. Math. Anal. Appl. 351 (2), 536–542, 2009.
11. 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.
12. 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).
13. 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.
14. 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.