SOLUTIONS OF FRATIONAL EMDEN-FOWLER EQUATIONS BY HOMOTOPY ANALYSIS METHOD
DOI:
https://doi.org/10.24297/jam.v13i1.5849Keywords:
fractional Emden-Fowler type equations, homotopy analysis method, Caputo fractional derivativeAbstract
In this paper, we have solved the singular initial value problems of fractional Emden-Fowler type equations by using the homotopy analysis method. The approximate analytical solution of this type equations are obtained.
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References
[1] Chowdhury,M.S.H,and I.Hashim, Solutions of Emden–Fowler equations by homotopy perturbation method,Nonlinear Analysis Real World Applications ,10(2009),1, pp.104-115.
[2] Wazwaz, Abdul Majid, A new algorithm for solving differential equations of Lane–Emden type, Applied Mathematics & Computation, 118(2001), 2-3,pp.287-310.
[3] Liao, Shijun, A new analytic algorithm of Lane–Emden type equations, Applied Mathematics & Computation ,142(2003),1, pp.1-16.
[4] Liao, Shijun, Homotopy analysis method: a new analytical technique for nonlinear problems, Communications in Nonlinear Science and Numerical Simulation, 2 (1997),2, pp.95-100.
[5] Wong, James SW, On the generalized Emden–Fowler equation, Siam Review, 17(1975),2, pp.339-360.
[6] Shang, Xufeng, Peng Wu, and Xingping Shao, An efficient method for solving Emden–Fowler equations, Journal of the Franklin Institute, 346(2009), 2, pp. 889-897.
[7] Băleanu, Dumitru, Octavian G. Mustafa, and Ravi P. Agarwal, An existence result for a superlinear fractional differential equation, Applied Mathematics Letters, 23 (2010),9, pp.1129-1132.
[8] Dehghan, Mehdi, and Fatemeh Shakeri, 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.
[9] Khan, Junaid Ali, Muhammad Asif Zahoor Raja, and Ijaz Mansoor Qureshi, Numerical treatment of nonlinear Emden–Fowler equation using stochastic technique, Annals of Mathematics and Artificial Intelligence ,63(2011),2,pp.185-207.
[10] Chowdhury, Md., 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.
[11] Wazwaz, Abdul-Majid, et al., Solving the Lane–Emden–Fowler type equations of higher orders by the Adomian decomposition method, Comput. Model. Eng. Sci.(CMES) 100(2014),6,pp. 507-529.
[12] Kaur, Harpreet, R. C. Mittal, and Vinod Mishra, Haar wavelet approximate solutions for the generalized Lane–Emden equations arising in astrophysics, Computer Physics Communications , 184(2013),9, pp.2169-2177.
[2] Wazwaz, Abdul Majid, A new algorithm for solving differential equations of Lane–Emden type, Applied Mathematics & Computation, 118(2001), 2-3,pp.287-310.
[3] Liao, Shijun, A new analytic algorithm of Lane–Emden type equations, Applied Mathematics & Computation ,142(2003),1, pp.1-16.
[4] Liao, Shijun, Homotopy analysis method: a new analytical technique for nonlinear problems, Communications in Nonlinear Science and Numerical Simulation, 2 (1997),2, pp.95-100.
[5] Wong, James SW, On the generalized Emden–Fowler equation, Siam Review, 17(1975),2, pp.339-360.
[6] Shang, Xufeng, Peng Wu, and Xingping Shao, An efficient method for solving Emden–Fowler equations, Journal of the Franklin Institute, 346(2009), 2, pp. 889-897.
[7] Băleanu, Dumitru, Octavian G. Mustafa, and Ravi P. Agarwal, An existence result for a superlinear fractional differential equation, Applied Mathematics Letters, 23 (2010),9, pp.1129-1132.
[8] Dehghan, Mehdi, and Fatemeh Shakeri, 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.
[9] Khan, Junaid Ali, Muhammad Asif Zahoor Raja, and Ijaz Mansoor Qureshi, Numerical treatment of nonlinear Emden–Fowler equation using stochastic technique, Annals of Mathematics and Artificial Intelligence ,63(2011),2,pp.185-207.
[10] Chowdhury, Md., 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.
[11] Wazwaz, Abdul-Majid, et al., Solving the Lane–Emden–Fowler type equations of higher orders by the Adomian decomposition method, Comput. Model. Eng. Sci.(CMES) 100(2014),6,pp. 507-529.
[12] Kaur, Harpreet, R. C. Mittal, and Vinod Mishra, Haar wavelet approximate solutions for the generalized Lane–Emden equations arising in astrophysics, Computer Physics Communications , 184(2013),9, pp.2169-2177.
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Published
2018-01-24
How to Cite
Wang, H. H., & Hu, Y. (2018). SOLUTIONS OF FRATIONAL EMDEN-FOWLER EQUATIONS BY HOMOTOPY ANALYSIS METHOD. JOURNAL OF ADVANCES IN MATHEMATICS, 13(1), 7042–7047. https://doi.org/10.24297/jam.v13i1.5849
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