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Chun-Fu Wei

APPLICATION OF THE HOMOTOPY PERTURBATION METHOD FOR SOLVING FRACTIONAL LANE-EMDEN TYPE EQUATION

ABSTRACT
A new algorithm is proposed in this paper, which is based on the homotopy perturbation method incorporating the Adomian decomposition method, to solve the non-linear and singular Lane-Emden type equations. Results of the numerical examples illustrate that the algorithm is remarkably effective.
KEYWORDS
fractional Lane-Emden type equations, homotopy perturbation method, Adomian decomposition method
PAPER SUBMITTED: 2018-03-22
PAPER REVISED: 2018-06-26
PAPER ACCEPTED: 2018-06-26
PUBLISHED ONLINE: 2019-09-14
DOI REFERENCE: https://doi.org/10.2298/TSCI1904237W
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Issue 4, PAGES [2237 - 2244]
REFERENCES
  1. Shawagfeh, N. T., Nonperturbative Approximate Solution for Lane-Emden Equation, Journal of Mathe-matical Physics, 34 (1993), 9, pp. 4364-4369
  2. Baranwal, V. K., et al., An Analytic Algorithm of Lane-Emden-Type Equations Arising in Astrophysics - a Hybrid Approach, Journal of Theoretical & Applied Physics, 6 (2012), 1, pp. 22-28
  3. Parand, K., et al., An Approximate Algorithm for the Solution of the Non-Linear Lane-Emden Type Equations Arising in Astrophysics Using Hermite Function Collocation Method, Computer Physics Communications, 181 (2010), 6, pp. 1096-1108
  4. Hasan, Y. Q., On the Numerical Solution of Lane-Emden Type Equations, Advances in Computational Mathematics & Its Applications, 1 (2012), 4, pp. 10-16
  5. Motsa, S. S., Shateyi, S. A., Successive Linearization Method Approach to Solve Lane-Emden Type of Equations. Mathematical Problems in Engineering, 10 (2012), 3, pp. 1627-1632
  6. Wazwaz, A. M., A New Algorithm for Solving Differential Equations of Lane-Emden Type, Applied Mathematics & Computation, 118 (2001), 2, pp. 287-310
  7. Rach, R., et al., Solving Coupled Lane-Emden Boundary Value Problems in Catalytic Diffusion Reac-tions by the Adomian Decomposition Method, Journal of Mathematical Chemistry, 52 (2014), 1, pp. 255-267
  8. Wazwaz, A. M., et al., Adomian Decomposition Method for Solving the Volterra Integral Form of the Lane-Emden Equations with Initial Values and Boundary Conditions, Applied Mathematics & Computa-tion, 219 (2013), 10, pp. 5004-5019
  9. Wazwaz, A. M., et al., A Study on the Systems of the Volterra Integral Forms of the Lane-Emden Equa-tions by the Adomian Decomposition Method, Mathematical Methods in the Applied Sciences, 37 (2014), 1, pp. 10-19
  10. Rach, R., Wazwaz, A. M., Higher Order Numeric Solutions of the Lane-Emden-Type Equations Derived from the Multi-Stage Modified Adomian Decomposition Method, International Journal of Computer Mathematics, 94 (2017), 1, pp. 197-215
  11. Ahmad, I., et al., Neural Network Methods to Solve the Lane-Emden Type Equations Arising in Ther-modynamic Studies of the Spherical Gas Cloud Model, Neural Computing & Applications, 21 (2016), 5, pp. 1-16
  12. Hosseini, M. M., Nasabzadeh, H., Modified Adomian Decomposition Method for Specific Second Order Ordinary Differential Equations, Applied Mathematics & Computation, 186 (2007), 1, pp. 117-123
  13. He, J.-H., Homotopy Perturbation Method: a New Non-Linear Analytical Technique, Applied Mathemat-ics and computation, 13 (2003), 1, pp. 73-79
  14. Hu, Y., He, J.-H., On Fractal Space-Time and Fractional Calculus, Thermal Science, 20 (2016), 3, pp. 773-777.
  15. Nasab, A. K., et al., A Numerical Method for Solving Singular Fractional Lane-Emden Type Equations, Journal of King Saud University - Science, 32 (2016), 3, pp. 13-21
  16. He, J.-H., Fractal Calculus and its Geometrical Explanation, Results in Physics, 10 (2018), Sept., pp. 272-276
  17. He, J.-H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, International Journal of Theoretical Physics, 53 (2014), 11, pp. 3698-3718
  18. He, J.-H., et al., Geometrical Explanation of the Fractional Complex Transform and Derivative Chain Rule for Fractional Calculus, Phys. Lett. A, 376 (2012), 4, pp. 257-259
  19. He, J.-H., Homotopy Perturbation Method with an Auxiliary Term, Abstract and Applied Analysis, 2012 (2012), Special Issue, ID 857612
  20. He, J.-H., Homotopy Perturbation Method with Two Expanding Parameters, Indian Journal of Physics, 88 (2014), 2, pp. 193-196
  21. Wu, Y., He, J.-H., Homotopy Perturbation Method for Non-Linear Oscillators with Coordinate Depend-ent Mass, Results in Physics, 10 (2018), Sept., pp. 270-271
  22. Wei, C. F., Solving Time-Space Fractional Fitzhugh-Nagumo Equation by Using He-Laplace Decompo-sition Method, Thermal Science, 22 (2018), 4, pp. 1723-1728
  23. Wang, K. L., Wang. K. J., A Modification of the Reduced Differential Transform Method for Fractional Calculus, Thermal Science, 22 (2018), 4, pp. 1871-1875
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Application of the homotopy perturbation method for solving fractional Lane-Emden type equation

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