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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 673829, 12 pages
http://dx.doi.org/10.1155/2013/673829
Research Article

A Reliable Analytical Method for Solving Higher-Order Initial Value Problems

1Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan
2Department of Mechatronics Engineering, Faculty of Engineering, University of Jordan, Amman 11942, Jordan
3Department of Mathematics, Faculty of Science, The Hashemite University, Zarqa 13115, Jordan
4Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan

Received 2 July 2013; Accepted 23 September 2013

Academic Editor: Recai Kilic

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 [15 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
  • 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, 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
  • 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
  • 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
  • Shaher Momani, Omar Abu Arqub, Ma'mon Abu Hammad, and Zaer S. Abo-Hammour, “A residual power series technique for solving systems of initial value problems,” Applied Mathematics and Information Sciences, vol. 10, no. 2, pp. 765–775, 2016. View at Publisher · View at Google Scholar
  • Fei Xu, Yixian Gao, Xue Yang, and He Zhang, “Construction of Fractional Power Series Solutions to Fractional Boussinesq Equations Using Residual Power Series Method,” Mathematical Problems in Engineering, vol. 2016, pp. 1–15, 2016. 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