Numerical treatment for the solution of fractional fifth-order Sawada-Kotera equation using second kind Chebyshev wavelet method

Applied Mathematical Modelling

Volumn 39, Issue 17, 2015, Pages 5121-5130

  Gupta, A K ^a   Saha Ray, S ^a  

^a NATIONAL INSTITUTE OF TECHNOLOGY   (India)

Author keywords

Caputo derivative; Chebyshev wavelet method; Fractional sawada kotera equation; Homotopy analysis method

Indexed keywords

NONLINEAR EQUATIONS;

CAPUTO DERIVATIVES; FRACTIONAL INTEGRATION; FRACTIONAL SAWADA-KOTERA EQUATION; HOMOTOPY ANALYSIS METHODS; NUMERICAL TREATMENTS; OPERATIONAL MATRICES; SECOND KIND CHEBYSHEV WAVELETS; WAVELET METHODS;

NUMERICAL METHODS;

EID: 84930752420     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2015.04.003     Document Type: Article

References (27)

1. Das S. Functional Fractional Calculus 2011, Springer-Verlag, Berlin.
2. Gupta A.K., Saha Ray S. On the solutions of fractional Burgers-Fisher and generalized Fisher's equations using two reliable methods. Int. J. Math. Math. Sci. 2014, 16. Article ID 682910.
3. Saha Ray S. On Haar wavelet operational matrix of general order and its application for the numerical solution of fractional Bagley Torvik equation. Appl. Math. Comput. 2012, 218:5239-5248.
4. Gupta A.K., Saha Ray S. Comparison between homotopy perturbation method and optimal homotopy asymptotic method for the soliton solution of Boussinesq-Burgers equation. Comput. Fluids 2014, 103:34-41.
5. Saha Ray S., Gupta A.K. A two-dimensional Haar wavelet approach for the numerical simulations of time and space fractional Fokker-Planck equations in modelling of anomalous diffusion systems. J. Math. Chem. 2014, 52(8):2277-2293. 10.1007/s10910-014-0384-3.
6. Liu F., Zhuang P., Burrage K. Numerical methods and analysis for a class of fractional advection-dispersion models. Comput. Math. Appl. 2012, 64:2990-3007.
7. Jiang H., Liu F., Turner I., Burrage I. Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain. J. Math. Anal. Appl. 2012, 389:1117-1127.
8. Saha Ray S., Gupta A.K. Numerical solution of fractional partial differential equation of parabolic type with Dirichlet boundary conditions using two-dimensional Legendre wavelets method. J. Comput. Nonlinear Dyn. 2014, (in Press). 10.1115/1.4028984.
9. Gupta A.K., Saha Ray S. Travelling wave solution of fractional KdV-Burger-Kuramoto equation describing nonlinear physical phenomena. AIP Adv. 2014, 4. 097120-1-11. 10.1063/1.4895910.
10. Sahu P.K., Saha Ray S. Legendre wavelets operational method for the numerical solutions of nonlinear Volterra integro-differential equations system. Appl. Math. Comput. 2015, 256:715-723.
11. Sahu P.K., Saha Ray S. Two dimensional Legendre wavelet method for the numerical solutions of fuzzy integro-differential equations. J. Intell. Fuzzy Syst. 2015, 28:1271-1279.
12. Zhu L., Fan Q. Solving fractional nonlinear Fredholm integro-differential equations by the second kind Chebyshev wavelet. Commun. Nonlinear Sci Numer. Simul. 2012, 17:2333-2341.
13. Wang Y., Fan Q. The second kind Chebyshev wavelet method for solving fractional differential equations. Appl. Math. Comput. 2012, 218:8592-8601.
14. '/G) method. Math. Prob. Eng. 2013, 13. Article ID 826369.
15. Nahar H., Abdullah F.A., Mohyud-Din S.T. Extended generalized Riccati equation mapping method for the fifth-order Sawada-Kotera equation. AIP Adv. 2013, 3:052104. 10.1063/1.4804433.
16. Dinarvand S., Khosravi S., Doosthoseini A., Rashidi M.M. The homotopy analysis method for solving the Sawada-Kotera and Lax's fifth-order KdV equations. Adv. Theor. Appl. Mech. 2008, 1(7):327-335.
17. Wazwaz A.M. Partial Differential Equations and Solitary Waves Theory 2009, Springer, Higher Education Press, Berlin.
18. Debnath L. Nonlinear Partial Differential Equations for Scientists and Engineers 2012, Birkhauser, Springer, New York.
19. Podlubny I. Fractional Differential Equations 1999, Academic Press, New York.
20. Samko S.G., Kilbas A.A., Marichev O.I. Fractional Integrals and derivatives: Theory and Applications 1993, Taylor and Francis, London.
21. Agarwal O.P. A general formulation and solution scheme for fractional optimal control problems. Nonlinear Dyn. 2004, 38:323-337.
22. Iyiola O.S. A numerical study of Ito equation and Sawada-Kotera equation both of time-fractional type. Adv. Math. Sci. J. 2013, 2(2):71-79.
23. Liao S. On the homotopy analysis method for nonlinear problems. Appl. Math. Comput. 2004, 147:499-513.
24. Saha Ray S., Patra A. Application of homotopy analysis method and adomian decomposition method for the solution of neutron diffusion equation in the hemisphere and cylindrical reactors. J. Nucl. Eng. Technol. 2011, 1(2-3):1-12.
25. Saadatmandi A., Dehghan M. A new operational matrix for solving fractional-order differential equations. Comput. Math. Appl. 2010, 59:1326-1336.
26. Dehghan M., Manafian J., Saadatmandi A. Solving nonlinear fractional partial differential equations using the homotopy analysis method. Numer. Methods Partial Differ. Equ. 2009, 26:448-479.
27. Dehghan M., Manafian J., Saadatmandi A. The solution of the linear fractional partial differential equations using the homotopy analysis method. Z. Naturforsch. A 2010, 65a(11):935-949.