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The fractional power series method was originally proposed to solve a fractional differential equation. This paper extends the method to a system of fractional differential equations with great success. How to construct an initial solution, plays an important role in the solution process and an example is given to elucidate the choice of the initial solution.
PAPER REVISED: 2017-08-23
PAPER ACCEPTED: 2017-09-01
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THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Issue 4, PAGES [1745 - 1751]
  1. Adomian, G., A Review of the Decomposition Method in Applied Mathematics, Journal of Mathemati-cal Analysis and Applications, 135 (1988), 2, pp. 501-544
  2. He, J. H., Homotopy Perturbation Method: A New Nonlinear Analytical Technique, Applied Mathemat-ics and Computation, 135, (2003), 1, pp. 73-79
  3. He, J. H., Variational Iteration Method-a Kind of Non-Linear Analytical Technique: Some Examples, In-ternational Journal of Non-Linear Mechanics, 34 (1999), 4, pp. 699-708
  4. Liao, S. J., Chwang, A. T., Application of Homotopy Analysis Method in Nonlinear Oscillations, Jour-nal of Applied Mechanics, 65 (1998), 4, pp. 914-922
  5. Wazwaz, A. M., A Comparison between Adomian Decomposition Method and Taylor Series Method in the Series Solutions, Applied Mathematics & Computation, 97 (1998), 1, pp. 37-44
  6. Daftardar-Gejji, V., Jafari, H., An Iterative Method for Solving Nonlinear Functional Equations, Jour-nal of Mathematical Analysis and Applications , 316 (2006), 2, pp. 753-763
  7. El-Ajou, A., et al., New Results on Fractional Power Series: Theories and Applications, Entropy, 15 (2013), 12, pp. 5305-5323
  8. Jafari, H., Daftardar-Gejji, V., Solving a System of Nonlinear Fractional Differential Equations Using Adomian Decomposition, Journal of Computational and Applied Mathematics, 196 (2006), 2, pp. 644-651
  9. Daftardar-Gejji, V., Jafari, H., Analysis of a System of Nonautonomous Fractional Differential Equa-tions Involving Caputo Derivatives, Journal of Mathematical Analysis and Applications, 328 (2007), 2, pp. 1026-1033
  10. Jafari, H., Seifi, S., Solving a System of Nonlinear Fractional Partial Differential Equations Using Ho-motopy Analysis Method,Communications in Nonlinear Science and Numerical Simulation, 14 (2009), 5, pp. 1962-1969
  11. Edwards, J. T., et al., The Numerical Solution of Linear Multi-Term Fractional Differential Equations: Systems of Equations, Journal of Computational and Applied Mathematics, 148 (2002), 2, pp. 401-418
  12. Momani, S., Al-Khaled, K., Numerical Solutions for Systems of Fractional Differential Equations by the Decomposition Method, Applied Mathematics and Computation, 162 (2005), 3, pp. 1351-1365
  13. Wazwaz, A.-M., The Decomposition Method Applied to Systems of Partial Differential Equations and to the Reaction-Diffusion Brusselator Model, Applied Mathematics and Computation, 110 (2000), 2, pp. 251-264
  14. Hu, Y., He, J.-H., On Fractal Space-Time and Fractional Calculus. Thermal Science, 20 (2016), 3, pp. 773-777
  15. Hu, Yue, Chebyshev Type Inequalities for General Fuzzy Integrals, Information Sciences, 278 (2014), 1, pp. 822-825
  16. Hilfer, R., Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000
  17. Caputo, M., Linear Models of Dissipation whose Q is Almost Frequency Independent, Part II, J. Roy. Astr. Soc., 13 (1967), 1, pp. 529-539

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