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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 378593, 10 pages
http://dx.doi.org/10.1155/2013/378593
Research Article

A Representation of the Exact Solution of Generalized Lane-Emden Equations Using a New Analytical Method

1Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan
2School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

Received 10 April 2013; Accepted 31 May 2013

Academic Editor: Massimo Furi

Copyright © 2013 Omar Abu Arqub et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [22 citations]

The following is the list of published articles that have cited the current article.

  • Ahmad El-Ajou, Omar Abu Arqub, and Zeyad Al Zhour, “New Results on Fractional Power Series: Theories and Applications,” Entropy, vol. 15, no. 12, pp. 5305–5323, 2013. View at Publisher · View at Google Scholar
  • Omar Abu Arqub, Zaer Abo-Hammour, Ramzi Al-Badarneh, and Shaher Momani, “A Reliable Analytical Method for Solving Higher-Order Initial Value Problems,” Discrete Dynamics in Nature and Society, vol. 2013, pp. 1–12, 2013. View at Publisher · View at Google Scholar
  • Ahmad El-Ajou, Omar Abu Arqub, and Shaher Momani, “Approximate analytical solution of the nonlinear fractional KdV-Burgers equation: A new iterative algorithm,” Journal of Computational Physics, 2014. View at Publisher · View at Google Scholar
  • Omar Abu Arqub, Ahmad El-Ajou, and Shaher Momani, “Construct and predict solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations,” Journal of Computational Physics, 2014. View at Publisher · View at Google Scholar
  • Omar Abu Arqub, Ahmad El-Ajou, Zeyad Al Zhour, and Shaher Momani, “Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique,” Entropy, vol. 16, no. 1, pp. 471–493, 2014. View at Publisher · View at Google Scholar
  • Zaer Abo-Hammour, Omar Abu Arqub, Othman Alsmadi, Shaher Momani, and Ahmed Alsaedi, “An optimization algorithm for solving systems of singular boundary value problems,” Applied Mathematics and Information Sciences, vol. 8, no. 6, pp. 2809–2821, 2014. View at Publisher · View at Google Scholar
  • Zaer Abo-Hammour, Omar Abu Arqub, Shaher Momani, and Nabil Shawagfeh, “Optimization Solution of Troesch’s and Bratu’s Problems of Ordinary Type Using Novel Continuous Genetic Algorithm,” Discrete Dynamics in Nature and Society, vol. 2014, pp. 1–15, 2014. View at Publisher · View at Google Scholar
  • Ahmad El-Ajou, Omar Abu Arqub, and Mohammed Al-Smadi, “A general form of the generalized Taylor’s formula with some applications,” Applied Mathematics and Computation, vol. 256, pp. 851–859, 2015. View at Publisher · View at Google Scholar
  • Ahmad El-Ajou, Omar Abu Arqub, Shaher Momani, Dumitru Baleanu, and Ahmed Alsaedi, “A novel expansion iterative method for solving linear partial differential equations of fractional order,” Applied Mathematics and Computation, 2015. View at Publisher · View at Google Scholar
  • Marwan Alquran, Kamel Al-Khaled, Tridip Sardar, and Joydev Chattopadhyay, “Revisited Fisher’s equation in a new outlook: A fractional derivative approach,” Physica A: Statistical Mechanics and its Applications, vol. 438, pp. 81–93, 2015. View at Publisher · View at Google Scholar
  • Khaled Moaddy, Mohammed AL-Smadi, and Ishak Hashim, “A Novel Representation of the Exact Solution for Differential Algebraic Equations System Using Residual Power-Series Method,” Discrete Dynamics in Nature and Society, vol. 2015, pp. 1–12, 2015. View at Publisher · View at Google Scholar
  • Zeliha S. Korpinar, Fairouz Tchier, Mustafa Inc, and Dumitru Baleanu, “Solutions of the time fractional reaction-diffusion equations with residual power series method,” Advances in Mechanical Engineering, vol. 8, no. 10, pp. 1–10, 2016. View at Publisher · View at Google Scholar
  • Mustafa Inc, Zeliha S. Korpinar, Maysaa' Mohamed Al Qurashi, and Dumitru Baleanu, “A new method for approximate solutions of some nonlinear equations: Residual power series method,” Advances In Mechanical Engineering, vol. 8, no. 4, 2016. View at Publisher · View at Google Scholar
  • Hira Tariq, and Ghazala Akram, “New traveling wave exact and approximate solutions for the nonlinear Cahn–Allen equation: evolution of a nonconserved quantity,” Nonlinear Dynamics, vol. 88, no. 1, pp. 581–594, 2016. View at Publisher · View at Google Scholar
  • Hira Tariq, and Ghazala Akram, “Residual power series method for solving time-space-fractional Benney-Lin equation arising in falling film problems,” Journal of Applied Mathematics and Computing, 2016. View at Publisher · View at Google Scholar
  • Iryna Komashynska, Omar Abu Arqub, Mohammed Al-Smadi, and Shaher Momani, “An efficient analytical method for solving singular initial value problems of nonlinear systems,” Applied Mathematics and Information Sciences, vol. 10, no. 2, pp. 647–656, 2016. View at Publisher · View at Google Scholar
  • Maysaa’ Mohamed Al Qurashi, Zeliha Korpinar, Dumitru Baleanu, and Mustafa Inc, “A new iterative algorithm on the time-fractional Fisher equation: Residual power series method,” Advances in Mechanical Engineering, vol. 9, no. 9, pp. 168781401771600, 2017. View at Publisher · View at Google Scholar
  • Maysaa Mohamed Al Qurashi, and Zeliha S. Korpinar, “Approximate solutions of bright and dark optical solitons in birefrigent fibers,” Optik, vol. 140, pp. 45–61, 2017. View at Publisher · View at Google Scholar
  • Faisal Ababneh, Joydev Chattopadhyay, Marwan Alquran, and Kamel Al-Khaled, “A New and Elegant Approach for Solving n×n -Order Linear Fractional Differential Equations,” Mediterranean Journal of Mathematics, vol. 14, no. 2, 2017. View at Publisher · View at Google Scholar
  • Bewar A. Mahmood, and Majeed A. Yousif, “A novel analytical solution for the modified Kawahara equation using the residual power series method,” Nonlinear Dynamics, 2017. View at Publisher · View at Google Scholar
  • Khaled K. Jaber, and Rami S. Ahmad, “Analytical solution of the time fractional Navier-Stokes equation,” Ain Shams Engineering Journal, 2017. View at Publisher · View at Google Scholar
  • Muhammed I. Syam, “Analytical Solution of the Fractional Fredholm Integrodifferential Equation Using the Fractional Residual Power Series Method,” Complexity, vol. 2017, pp. 1–6, 2017. View at Publisher · View at Google Scholar