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In this paper, we presented a reliable algorithm to solve the singularity initial value problems of the time-dependent fractional Emden-Fowler type equations by homotopy analysis method. The approximate solutions of the problems are obtained.
PAPER REVISED: 2017-05-01
PAPER ACCEPTED: 2017-06-28
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THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Supplement 1, PAGES [S113 - S120]
  1. Yang, X. J., et al., Local Fractional Integral Transforms and their Applications, Academic Press, New York, USA, 2005
  2. Yang, X. J., General Fractional Derivatives: A Tutorial Comment, Proceedings, Symposium on Advanced Computational Methods for Linear and Nonlinear Heat and Fluid Flow 2017 & Advanced Computational Methods in Applied Science 2017& Fractional (Fractal) Calculus and Applied Analysis 2017, Songjiang, Shanghai, China
  3. Yang, X. J., et al., Anomalous Diffusion Models with General Fractional Derivatives within the Kernels of the Extended Mittag-Leffler Type Functions, Romanian Reports in Physics, 69 (2017), 4, 115
  4. Yang, X. J., New Rheological Problems Involving General Fractional Derivatives within Nonsingular Power-Law Kernel, Proceedings of the Romanian Academy - Series A, 69 (2017), 3, in press
  5. Yang, X. J., et al., A New Fractional Operator of Variable Order: Application in the Description of Anomalous Diffusion, Physica A: Statistical Mechanics and its Applications, 481 (2017), Sept., pp. 276-283
  6. Yang, X. J., Fractional Derivatives of Constant and Variable Orders Applied to Anomalous Relaxation Models in Heat-Transfer Problems, Thermal Science, 21 (2017), 3, pp. 1161-1171
  7. Wang, H. H., Hu, Y., Solutions of Fractional Emden-Fowler Equations by Homotopy Analysis Method, Journal of Advances in Mathematics, 13 (2017), 1, pp. 7042-7047
  8. Chowdhury, M. S. H., Hashim, I., Solutions of Emden-Fowler Equations by Homotopy Perturbation Method, Nonlinear Analysis Real World Applications, 10 (2009), 1, pp. 104-115
  9. Wazwaz, A. M., A New Algorithm for Solving Differential Equations of Lane-Emden Type, Applied Mathematics & Computation, 118 (2001), 2-3, pp. 287-310
  10. Wong, J. S. W., On the Generalized Emden-Fowler Equation, Siam Review, 17 (1975), 2, pp. 339-360
  11. Shang, X, et al., An Efficient Method for Solving Emden-Fowler Equations, Journal of the Franklin Institute, 346 (2009), 2, pp. 889-897
  12. Liao, S. J., Homotopy Analysis Method: a New Analytical Technique for Nonlinear Problems, Communications in Nonlinear Science and Numerical Simulation, 2 (1997), 2, pp. 95-100
  13. Baleanu, D., et al., An Existence Result for a Superlinear Fractional Differential Equation, Applied Mathematics Letters, 23 (2010), 9, pp. 1129-1132
  14. Dehghan, M., Fatemeh S., Solution of an Integro-Differential Equation Arising in Oscillating Magnetic Fields Using He's Homotopy Perturbation Method, Progress in Electromagnetics Research, 78 (2008), 1, pp. 361-376
  15. Khan, J. A., et al., Numerical Treatment of Nonlinear Emden-Fowler Equation Using Stochastic Technique, Annals of Mathematics and Artificial Intelligence, 63 (2011), 2, pp. 185-207
  16. Chowdhury, S. H., A Comparison between the Modified Homotopy Perturbation Method and Adomian Decomposition Method for Solving Nonlinear Heat Transfer Equations, Journal of Applied Sciences, 11 (2011), 7, pp. 1416-1420
  17. Wazwaz, A. M, et al., Solving the Lane-Emden-Fowler Type Equations of Higher Orders by the Adomian Decomposition Method, Computer Modeling in Engineering & Sciences, 100 (2014), 6, pp. 507-529
  18. Kaur, H, et al., Haar Wavelet Approximate Solutions for the Generalized Lane-Emden Equations Arising in Astrophysics, Computer Physics Communications, 184 (2013), 9, pp. 2169-2177
  19. Hilfer, R., Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000, pp. 1021-1032
  20. Yang, X. J., New General Fractional-Order Rheological Models within Kernels of Mittag-Leffler Functions, Romanian Reports in Physics, 69 (2017), 4, 118
  21. Yang, X. J., et al., Some New Applications for Heat and Fluid Flows Via Fractional Derivatives without Singular Kernel, Thermal Science, 20 (2016), Suppl. 3, pp. S833-S839
  22. Gao, F., et al., Fractional Maxwell Fluid with Fractional Derivative without Singular Kernel, Thermal Science, 20 (2016), Suppl. 3, pp. S871-S877
  23. Yang, X. J., et al., A New Fractional Derivative without Singular Kernel: Application to the Modelling of the Steady Heat Flow, Thermal Science, 20 (2016), 2, pp. 753-756
  24. Yang, A. M., et al., On Steady Heat Flow Problem Involving Yang-Srivastava-Machado Fractional Derivative without Singular Kernel, Thermal Science, 20 (2016), Suppl. 3, pp. S717-S721

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