The approximate and exact solutions of the fractional-order delay differential equations using Legendre seudospectral method

International Journal of Pure and Applied Mathematics

Volumn 74, Issue 3, 2012, Pages 287-297

  Khader, M M ^a   Hendy, A S ^a  

^a BENHA UNIVERSITY   (Egypt)

Author keywords

Caputo fractional derivatives; Fractional delay differential equations; Legendre polynomials

Indexed keywords

EID: 84857583048     PISSN: 13118080     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. R. L. Bagley, P. J. Torvik, On the appearance of the fractional derivative in the behavior of real materials, J. Appl. Mech., 51(1984), 294-298. (Pubitemid 14583152)
2. W. W. Bell, Special Functions For Scientists and Engineers, Great Britain, Butler and Tanner Ltd, Frome and London (1968).
3. S. Das, Functional Fractional Calculus for System Identification and Controls, Springer, New York (2008).
4. K. Diethelm, An algorithm for the numerical solution of differential equations of fractional order, Electron. Trans. Numer. Anal., 5(1997), 1-6. (Pubitemid 38870919)
5. M. Enelund, B. L. Josefson, Time-domain finite element analysis of viscoelastic structures with fractional derivatives constitutive relations, AIAA J., 35, No. 10(1997), 1630-1637. (Pubitemid 127543041)
6. I. Hashim, O. Abdulaziz, S. Momani, Homotopy analysis method for fractional IVPs, Commun. Nonlinear Sci. Numer. Simul., 14(2009), 674-684.
7. J. H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Computer Methods in Applied Mechanics and Engineering, 167, No-s: 1-2(1998), 57-68.
8. J. H. He, Variational iteration method - A kind of non-linear analytical technique: Some examples, International Journal of Non-Linear Mechanics, 34(1999), 699-708.
9. J. H. He, Homotopy perturbation technique, Comput. Methods Appl. Mech. Engng., 178, No-s: 3-4(1999), 257-262.
10. M. Inc, The approximate and exact solutions of the space-and time-fractional Burger's equations with initial conditions by variational iteration method, J. Math. Anal. Appl., 345(2008), 476-484.
11. H. Jafari, V. Daftardar-Gejji, Solving linear and nonlinear fractional diffusion and wave equations by Adomian decomposition, Appl. Math. and Comput., 180(2006), 488-497. (Pubitemid 44441534)
12. M. M. Khader, On the numerical solutions for the fractional diffusion equation, Communications in Nonlinear Science and Numerical Simulation, 16(2011), 2535-2542.
13. M. M. Meerschaert, C. Tadjeran, Finite difference approximations for fractional advection-dispersion flow equations, J. Comput. Appl. Math., 172, No. 1(2004), 65-77. (Pubitemid 39204390)
14. I. Podlubny, Fractional Differential Equations, Academic Press, New York (1999).
15. M. A. Ramadan, Spline solution of first order delay differential equation, J. Egypt. Math. Soc., 1(2005), 7-18.
16. M. A. Ramdan, M. N. Shrif, Numerical solution of system of first order delay differential equations using spline functions, International Journal of Computer Mathematics, 83, No. 12(2006), 925-937.
17. E. A. Rawashdeh, Numerical solution of fractional integro-differential equations by collocation method, Appl. Math. Comput., 176(2006), 1-6.
18. S. Samko, A. Kilbas, O. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, London (1993).
19. N. H. Sweilam, M. M. Khader, R. F. Al-Bar, Numerical studies for a multiorder fractional differential equation, Physics Letters A, 371(2007), 26-33.
20. N. H. Sweilam, M. M. Khader, R. F. Al-Bar, Homotopy perturbation method for linear and nonlinear system of fractional integro-differential equations, Int. J. of Computational Mathematics and Numerical Simulation, 1, No. 1(2008), 73-87.
21. N. H. Sweilam, M. M. Khader, A. M. Nagy, Numerical solution of two-sided space fractional wave equation using finite difference method, Comput. and Applied Mathematics, 235(2011), 2832-2841.