Analytical Solution of the Fractional Initial Emden–Fowler Equation Using the Fractional Residual Power Series Method
- 52 Downloads
In this paper, we study the solution of the fractional initial Emden–Fowler equation which is a generalization to the initial Emden–Fowler equation. We implement the fractional power series method (RPS) to approximate the solution of this problem. Several examples are presented to show the accuracy of the presented technique.
KeywordsFractional Emden–Fowler equation Caputo derivative Generalized Taylor series Residual power series
The author also would like to express his sincere appreciation to the United Arab Emirates University Research Affairs for the financial support of Grant No. SURE Plus 21. Also, the author would like to express his sincere grateful to the reviewers for their valuable comments.
Compliance with ethical standards
Conflict of interest
The author declares that there is no conflict of interest regarding the publication of this paper.
- 11.Irandoust-pakchin, S., Abdi-Mazraeh, S.: Exact solutions for some of the fractional integrodifferential equations with the nonlocal boundary conditions by using the modification of He’s variational iteration method. Int. J. Adv. Math. Sci. 1(3), 139–144 (2013)Google Scholar
- 13.Mittal, R.C., Nigam, R.: Solution of fractional integrodifferential equations by Adomain decomposition method. Int. J. Appl. Math. Mech. 4(2), 87–94 (2008)Google Scholar
- 14.Saeedi, H., Samimi, F.: He’s homotopy perturbation method for nonlinear ferdholm integrodifferential equations of fractional order. Int. J. Eng. Res. Appl. 2(5), 52–56 (2012)Google Scholar
- 15.Saeed, R.K., Sdeq, H.M.: Solving a system of linear fredholm fractional integrodifferential equations using homotopy perturbation method. Aust. J. Basic Appl. Sci. 4(4), 633–638 (2010)Google Scholar
- 17.Abu Arqub, O., El-Ajou, A., Bataineh, A., Hashim, I.: A representation of the exact solution of generalized Lane Emden equations using a new analytical method 2013, Article ID 378593, 10 pages (2103)Google Scholar
- 23.Syam, M., Siyyam, H., Al-Subaihi, I., Tau-Path following method for solving the Riccati equation with fractional order. J. Comput. Methods Phys. 2014, Article ID 207916 (2014)Google Scholar