`Mathematical Problems in EngineeringVolume 2011, Article ID 587068, 14 pageshttp://dx.doi.org/10.1155/2011/587068`
Research Article

## Solution to the Linear Fractional Differential Equation Using Adomian Decomposition Method

1Department of Mathematics, Xiamen University, Xiamen 361005, China
2Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China

Received 25 March 2010; Accepted 1 June 2010

Copyright © 2011 Jin-Fa Cheng and Yu-Ming Chu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Application, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
2. K. Diethelm and N. J. Ford, “Numerical solution of the Bagley-Torvik equation,” BIT, vol. 42, no. 3, pp. 490–507, 2002.
3. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993.
4. A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions. Vol. III, McGraw-Hill, London, UK, 1955.
5. S. S. Ray and R. K. Bera, “Analytical solution of the Bagley Torvik equation by Adomian decomposition method,” Applied Mathematics and Computation, vol. 168, no. 1, pp. 398–410, 2005.
6. K. Diethelm and N. J. Ford, “Analysis of fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 265, no. 2, pp. 229–248, 2002.
7. K. Diethelm, “An algorithm for the numerical solution of differential equations of fractional order,” Electronic Transactions on Numerical Analysis, vol. 5, pp. 1–6, 1997.
8. J. Biazar, E. Babolian, and R. Islam, “Solution of the system of ordinary differential equations by Adomian decomposition method,” Applied Mathematics and Computation, vol. 147, no. 3, pp. 713–719, 2004.
9. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, Switzerland, 1993.
10. B. J. West, M. Bologna, and P. Grigolini, Physics of Fractal Operators, Springer, New York, NY, USA, 2003.
11. T. M. Atanackovic and B. Stankovic, “On a system of differential equations with fractional derivatives arising in rod theory,” Journal of Physics A, vol. 37, no. 4, pp. 1241–1250, 2004.
12. Y. Hu, Y. Luo, and Z. Lu, “Analytical solution of the linear fractional differential equation by Adomian decomposition method,” Journal of Computational and Applied Mathematics, vol. 215, no. 1, pp. 220–229, 2008.
13. G. Adomian, “A review of the decomposition method in applied mathematics,” Journal of Mathematical Analysis and Applications, vol. 135, no. 2, pp. 501–544, 1988.
14. G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, vol. 60 of Fundamental Theories of Physics, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994.
15. V. Daftardar-Gejji and H. Jafari, “Adomian decomposition: a tool for solving a system of fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 301, no. 2, pp. 508–518, 2005.
16. J.-H. He, G.-Ch. Wu, and F. Austin, “The variational iteration method which should be followed,” Nonlinear Science Letters A, vol. 1, no. 1, pp. 1–30, 2010.
17. S. Barat, S. Das, and P. K. Gupta, “A note on fractional schrodinger equation,” Nonlinear Science Letters A, vol. 1, no. 1, pp. 91–94, 2010.
18. A. E. Ebaid, “Exact orbits of planetary motion using the Adomian decomposition method,” Nonlinear Science Letters A, vol. 1, no. 3, pp. 249–252, 2010.
19. S. Das, “Solution of fractional vibration equation by the variational iteration method and modified decomposition method,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 9, no. 4, pp. 361–366, 2008.
20. A. Golbabai and K. Sayevand, “The homotopy perturbation method for multi-order time fractional differential equations,” Nonlinear Science Letters A, vol. 1, no. 2, pp. 147–154, 2010.
21. Y. Keskin and G. Oturanc, “The reduced differential transform method: a new approach to factional partial differential equations,” Nonlinear Science Letters A, vol. 1, no. 2, pp. 207–217, 2010.