Analytical solution of the Bagley Torvik equation by Adomian decomposition method

Applied Mathematics and Computation

Volumn 168, Issue 1, 2005, Pages 398-410

  Ray, S Saha ^a   Bera, R K ^b  

^a B P PODDAR INSTITUTE OF MANAGEMENT AND TECHNOLOGY   (India)

^b HERITAGE INSTITUTE OF TECHNOLOGY   (India)

Author keywords

Adomian decomposition method; Bagley Torvik equation; Fractional derivative; Fractional differential equation

Indexed keywords

CREEP; DAMPING; DECOMPOSITION; DIFFERENTIAL EQUATIONS; FUNCTIONS; GRAPH THEORY; MAGNETOELECTRIC EFFECTS; NEWTONIAN FLOW; PLATES (STRUCTURAL COMPONENTS); VISCOELASTICITY;

ADOMIAN DECOMPOSITION METHOD; BAGLEY-TORVIK EQUATION; FRACTIONAL DERIVATIVE; FRACTIONAL DIFFERENTIAL EQUATION;

PROBLEM SOLVING;

EID: 25644439033     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.09.006     Document Type: Article

References (41)

1. R.L. Bagley, and P.J. Torvik On the appearance of the fractional derivative in the behavior of real materials ASME J. Appl. Mech. 51 1984 294 298
2. I. Podlubny Fractional Differential Equations 1999 Academic Press San Diego, CA, USA
3. K.B. Oldham, and J. Spanier The Fractional Calculus 1974 Academic Press New York, London
4. K.B. Miller, and B. Ross An Introduction to the Fractional Calculus and Fractional Differential Equations 1993 John Wiley and Sons Inc. New York
5. K. Diethelm An algorithm for the numerical solution of differential equations of fractional order Electron. Transact. Numer. Anal. 5 1997 1 6
6. K. Diethelm, A.D. Freed, The FracPECE subroutine for the numerical solution of differential equations of fractional order, no. 52 in: S. Heinzel, T. Plesser (Eds.), GWDG-Berichte, Forschung und wissenschaftliches Rechnen: Beiträge zum Heinz-Billing-Preis 1998, Gesellschaft für wissenschaftliche Datenverarbeitung, Göttingen, pp. 57-71, 1999.
7. K. Diethelm, and N.J. Ford Analysis of fractional differential equations J. Math. Anal. Appl. 265 2002 229 248
8. K. Diethelm, N.J. Ford, and A.D. Freed A predictor-corrector approach for the numerical solution of fractional differential equations Nonlinear Dyn. 29 2002 3 22
9. K. Diethelm, N.J. Ford, Numerical Solution of the Bagley-Torvik Equation, BIT (to appear).
10. K. Diethelm, and A.D. Ford On the solution of nonlinear fractional-order differential equations used in the modeling of viscoplasticity, Scientific computing in chemical engineering II F. Keil W. Mackens H. Voß J. Werther Computational Fluid Dynamics, Reaction Engineering, and Molecular Properties 1999 Springer-Verlag Heidelberg 217 224
11. K. Diethelm, N.J. Ford, The numerical solution of linear and nonlinear fractional differential equations involving fractional derivatives of several orders, Numerical Analysis Report 379, Manchester Centre for Computational Mathematics, Manchester, England, 2001.
12. C. Trinks, and P. Ruge Treatment of dynamic systems with fractional derivatives without evaluating memory-integrals Comput. Mech. 29 6 2002 471 476
13. S. Saha Ray, R.K. Bera, Analytical solution of a dynamic system containing fractional derivative of order 1/2 by Adomian decomposition method, ASME Journal of Applied Mechanics, USA, 2004 (accepted).
14. G. Adomian Nonlinear Stochastic Systems Theory and Applications to Physics 1989 Kluwer Academic publishers Netherlands
15. G. Adomian Solving Frontier Problems of Physics: The Decomposition method 1994 Kluwer Academic Publishers Boston
16. G. Adomian An analytical solution of the stochastic Navier-Stokes system Found. Phys. 21 7 1991 831 843
17. G. Adomian, and R. Rach Linear and nonlinear Schrödinger equations Found. Phys. 21 1991 983 991
18. G. Adomian Solution of physical problems by decomposition Comput. Math. Appl. 27 9/10 1994 145 154
19. G. Adomian Solutions of nonlinear P.D.E. Appl. Math. Lett. 11 3 1998 121 123
20. K. Abbaoui, and Y. Cherruault The decomposition method applied to the Cauchy problem Kybernetes 28 1999 103 108
21. D. Kaya, and A. Yokus A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations Math. Comp. Simul. 60 6 2002 507 512
22. A. Wazwaz A reliable modification of Adomian decomposition method Appl. Math. Comp. 102 1 1999 77 86
23. D. Kaya, and S.M. El-Sayed On a generalized fifth order KdV equations Phys. Lett. A 310 1 2003 44 51
24. D. Kaya, and S.M. El-Sayed An application of the decomposition method for the generalized KdV and RLW equations Chaos, Solitons & Fractals 17 5 2003 869 877
25. D. Kaya An explicit and numerical solutions of some fifth-order KdV equation by decomposition method Appl. Math. Comp. 144 2-3 2003 353 363
26. D. Kaya A numerical simulation of solitary-wave solutions of the generalized regularized long-wave equation Appl. Math. Comp. 149 3 2004 833 841
27. A.J. George, and A. Chakrabarti The adomian method applied to some extraordinary differential equations Appl. Math. Lett. 8 3 1995 91 97
28. H.L. Arora, and F.I. Abdelwahid Solutions of non-integer order differential equations via the adomian decomposition method Appl. Math. Lett. 6 1 1993 21 23
29. N.T. Shawagfeh The decomposition method for fractional differential equations J. Frac. Calc. 16 1999 27 33
30. N.T. Shawagfeh Analytical approximate solutions for nonlinear fractional differential equations Appl. Math. Comp. 131 2002 517 529
31. S. Saha Ray, R.K. Bera, Solution of an extraordinary differential equation by Adomian decomposition method, J. Appl. Math. USA (in press).
32. S. Saha Ray, R.K. Bera, An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method, Appl. Math. Comput. USA (accepted).
33. V. Seng, K. Abbaoui, and Y. Cherruault Adomian's polynomials for nonlinear operators Math. Comput. Model. 24 1 1996 59 65
34. F. Abdelwahid A mathematical model of Adomian polynomials Appl. Math. Comp. 141 2003 447 453
35. Y. Cherruault Convergence of Adomian's method Kybernetes 18 1989 31 38
36. K. Abbaoui, and Y. Cherruault Convergence of Adomian's method applied to differential equations Comput. Math. Applic. 28 5 1994 103 109
37. K. Abbaoui, and Y. Cherruault New ideas for proving convergence of decomposition methods Comput. Math. Applic. 29 1995 103 108
38. N. Himoun, K. Abbaoui, and Y. Cherruault New results of convergence of Adomian's method Kybernetes 28 4-5 1999 423 429
39. C.F. Lorenzo, T.T. Hartley, Initialisation conceptualization, and application in the generalized fractional calculus, TM 1998-208415, NASA, NASA Center for Aerospace Information, 7121 Stadard Drive, Hanover, MD 21076, USA, 1998.
40. C.F. Lorenzo, and T.T. Hartley Initialised fractional calculus Int. J. Appl. Math. 3 3 2000 249 265
41. C.F. Lorenzo, T.T. Hartley, Initialization in fractional order systems, in: Proceedings of the European Control Conference, Porto, Portugal, pp. 1471-1476, 2001.