An analytical scheme for multi-order fractional differential equations

Tamsui Oxford Journal of Mathematical Sciences

Volumn 26, Issue 3, 2010, Pages 305-320

  Jaradat, H M ^a   Awawdeh, Fadi ^b   Rawashdeh, E A ^c  

^a AL AL BAYT UNIVERSITY   (Jordan)

^b HASHEMITE UNIVERSITY   (Jordan)

^c DHOFAR UNIVERSITY   (Oman)

Author keywords

Analytic solution; Multi order fractional differential equations

Indexed keywords

EID: 78649413544     PISSN: None     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. S. Abbasbandy, Soliton solutions for the Fitzhugh-Nagumo equation with the homotopy analysis method, Appl. Math. Model., 32(2008), 2706-2714.
2. F. Awawdeh, H. M. Jaradat, and O. Alsayyed, Solving system of DAEs by homotopy analysis method, Chaos Solitons Fract, 42(2009), 1422-1427.
3. R. L. Bagley and P. J. Torvik, On the appearance of the fractional derivative in the behaviour of real materials, J. Appl. Mech., 51(1984), 294-298.
4. L. Blank, Numerical treatment of differential equations of fractional order, Numerical Analysis Report 287, Manchester Center of Computational Mathematics, 1996.
5. K. Diethelm, An algorithm for the numerical solution of differential equations of fractional order, Elec. Transact. Numer. Anal., 5(1997), 1-6.
6. K. Diethelm and N. J. Ford, Multi-order fractional differential equations and their numerical solution, Appl. Math. Comp., 154(2004), 621-640.
7. K. Diethelm and N. J. Ford, Numerical solution of the Bagley-Torvik equation, BIT, 42(2002), 490-507.
8. K. Diethelm and N. J. Ford, Multi-order fractional differential equations and their numerical solution, Appl. Math. Comp., 154(2004), 621-640.
9. K. Diethelm, N. J. Ford, and A. D. Freed, Detailed error analysis for a fractional Adams method, Numer Algor., 36(2004), 31-52.
10. K. Diethelm, N. J. Ford, A. D. Freed, and Y. Luchko, Algorithms for the fractional calculus: A selection of numerical methods, Comput. Methods Appl. Mech. Engrg., 194(2005), 743-773.
11. N. J. Ford and J. A. Connolly, Comparison of numerical methods for fractional differential equations, Comm. Pure Appl. Anal., 5(2006), 289- 307.
12. N. J. Ford and J. A. Connolly, Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations, J. Comput. Appl. Math., 229(2009), 382-391.
13. T. Hayat and M. Sajid, On analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder, Phys. Lett. A., 361(2007), 316-322.
14. M. Inc, Application of homotopy analysis method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity, Math. Comput. Simul. (2008), doi:10.1016/j.matcom.2007.11.009.
15. M. Inc, On numerical solution of Burgers' equation by homotopy analysis method, Phys. Lett. A., 372(4)(2008), 356-360.
16. M. Inc, On exact solution of Laplace equation with Dirichlet and Neumann boundary conditions by the homotopy analysis method, Phys. Lett. A., 365(5-6) (2007), 412-415.
17. M. Inc, Application of homotopy analysis method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity, Math. Comput. Simulat., 79(2)(2008), 189-200.
18. S. J. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman & Hall/CRC Press, Boca Raton, 2003.
19. S. J. Liao, Notes on the homotopy analysis method: some definitions and theorems, Commun Nonlinear Sci Numer Simul, 14(2009), 983-997.
20. S. J. Liao, On the homotopy analysis method for nonlinear problems, Appl. Math. Comput., 147(2004), 499-513.
21. S. J. Liao and Y. Tan, A general approach to obtain series solutions of nonlinear differential equations, Stud. Appl. Math., 119(2007), 297-355.
22. F. Mainardi, Fractional calculus: Some basic problems in continuum and statistical mechanics, in Fractals and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F. Mainardi, eds., Wein, 1997, Springer, pp. 291-348.