Solution to the linear fractional differential equation using adomian decomposition method

Mathematical Problems in Engineering

Volumn 2011, Issue , 2011, Pages

  Cheng, Jin Fa ^a   Chu, Yu Ming ^b  

^a XIAMEN UNIVERSITY   (China)

^b HUZHOU UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ADOMIAN DECOMPOSITION METHOD; ANALYTICAL GENERAL SOLUTIONS; CAPUTO FRACTIONAL DERIVATIVES; CONSTANT COEFFICIENTS; INITIAL VALUES; LINEAR FRACTIONAL DIFFERENTIAL EQUATIONS; NON-HOMOGENEOUS;

ASYMPTOTIC STABILITY; OPERATIONS RESEARCH;

DIFFERENTIAL EQUATIONS;

EID: 77956961232     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2011/587068     Document Type: Article

References (21)

1. Podlubny I., Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Application 1999 198 San Diego, Calif, USA Academic Press xxiv+340 Mathematics in Science and Engineering
2. Diethelm K., Ford N. J., Numerical solution of the Bagley-Torvik equation BIT 2002 42 3 490 507
3. Miller K. S., Ross B., An Introduction to the Fractional Calculus and Fractional Differential Equations 1993 New York, NY, USA John Wiley Sons xvi+366
4. Erdlyi A., Magnus W., Oberhettinger F., Tricomi F. G., Higher Transcendental Functions. Vol. III 1955 London, UK McGraw-Hill xvii+292
5. Ray S. S., Bera R. K., Analytical solution of the Bagley Torvik equation by Adomian decomposition method Applied Mathematics and Computation 2005 168 1 398 410
6. Diethelm K., Ford N. J., Analysis of fractional differential equations Journal of Mathematical Analysis and Applications 2002 265 2 229 248
7. Diethelm K., An algorithm for the numerical solution of differential equations of fractional order Electronic Transactions on Numerical Analysis 1997 5 1 6 (Pubitemid 38870919)
8. Biazar J., Babolian E., Islam R., Solution of the system of ordinary differential equations by Adomian decomposition method Applied Mathematics and Computation 2004 147 3 713 719
9. Samko S. G., Kilbas A. A., Marichev O. I., Fractional Integrals and Derivatives: Theory and Applications 1993 Yverdon, Switzerland Gordon and Breach xxxvi+976
10. West B. J., Bologna M., Grigolini P., Physics of Fractal Operators 2003 New York, NY, USA Springer x+354
11. Atanackovic T. M., Stankovic B., On a system of differential equations with fractional derivatives arising in rod theory Journal of Physics A 2004 37 4 1241 1250
12. Hu Y., Luo Y., Lu Z., Analytical solution of the linear fractional differential equation by Adomian decomposition method Journal of Computational and Applied Mathematics 2008 215 1 220 229
13. Adomian G., A review of the decomposition method in applied mathematics Journal of Mathematical Analysis and Applications 1988 135 2 501 544
14. Adomian G., Solving Frontier Problems of Physics: The Decomposition Method 1994 60 Dordrecht, The Netherlands Kluwer Academic Publishers xiv+352 Fundamental Theories of Physics
15. Daftardar-Gejji V., Jafari H., Adomian decomposition: a tool for solving a system of fractional differential equations Journal of Mathematical Analysis and Applications 2005 301 2 508 518 (Pubitemid 39630973)
16. He J.-H., Wu G.-Ch., Austin F., The variational iteration method which should be followed Nonlinear Science Letters A 2010 1 1 1 30
17. Barat S., Das S., Gupta P. K., A note on fractional schrodinger equation Nonlinear Science Letters A 2010 1 1 91 94
18. Ebaid A. E., Exact orbits of planetary motion using the Adomian decomposition method Nonlinear Science Letters A 2010 1 3 249 252
19. Das S., Solution of fractional vibration equation by the variational iteration method and modified decomposition method International Journal of Nonlinear Sciences and Numerical Simulation 2008 9 4 361 366
20. Golbabai A., Sayevand K., The homotopy perturbation method for multi-order time fractional differential equations Nonlinear Science Letters A 2010 1 2 147 154
21. Keskin Y., Oturanc G., The reduced differential transform method: a new approach to factional partial differential equations Nonlinear Science Letters A 2010 1 2 207 217