Numerical Study of Fractional Differential Equations of Lane-Emden Type by Method of Collocation

Lane-Emden differential equations of order fractional has been studied.Numerical solution of this type is considered by collocation method. Some of examples are illustrated. The comparison between numerical and analytic methods has been introduced.

[1]  W. Mccrea An Introduction to the Study of Stellar Structure , 1939, Nature.

[2]  M. Darus,et al.  Subordination and superordination for analytic functions involving fractional integral operator , 2008 .

[3]  Margarita Rivero,et al.  On systems of linear fractional differential equations with constant coefficients , 2007, Appl. Math. Comput..

[4]  Rabha W. Ibrahim,et al.  On a fractional integral equation of periodic functions involving Weyl–Riesz operator in Banach algebras , 2008 .

[5]  Ravi P. Agarwal,et al.  Existence Theory for Singular Initial and Boundary Value Problems: A Fixed Point Approach , 2002 .

[6]  Rabha W. Ibrahim,et al.  On the existence and uniqueness of solutions of a class of fractional differential equations , 2007 .

[7]  I. Podlubny Fractional differential equations , 1998 .

[8]  Ravi P. Agarwal,et al.  Existence theory for single and multiple solutions to singular positone boundary value problems , 2001 .

[9]  Ali H. Bhrawy,et al.  A Jacobi–Gauss collocation method for solving nonlinear Lane–Emden type equations , 2012 .

[10]  Quadratic Forms and Nonlinear Non-Resonant Singular Second Order Boundary Value Problems of Limit Circle Type , 2001 .

[11]  N. Ford,et al.  Analysis of Fractional Differential Equations , 2002 .

[12]  H. J. Lane On the theoretical temperature of the Sun, under the hypothesis of a gaseous mass maintaining its volume by its internal heat, and depending on the laws of gases as known to terrestrial experiment , 1870, American Journal of Science and Arts.

[13]  Kourosh Parand,et al.  SINC-COLLOCATION METHOD FOR SOLVING ASTROPHYSICS EQUATIONS , 2010 .

[14]  M. M. Coclite,et al.  On a singular nonlinear dirichlet problem , 1989 .

[15]  Fajun Yu,et al.  Integrable coupling system of fractional soliton equation hierarchy , 2009 .

[16]  Md. Sazzad Hossien Chowdhury,et al.  Solutions of Emden-Fowler equations by homotopy-perturbation method , 2009 .

[17]  A. Yildirim,et al.  Solutions of singular IVPs of Lane–Emden type by the variational iteration method , 2009 .

[18]  Ercan Çelik,et al.  The Numerical Method for Solving Differential Equations of Lane-Emden Type by Padé Approximation , 2011 .

[19]  Mehdi Dehghan,et al.  An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method , 2010, Comput. Phys. Commun..

[20]  Ebrahim Momoniat,et al.  An implicit series solution for a boundary value problem modelling a thermal explosion , 2011, Math. Comput. Model..

[21]  Hojatollah Adibi,et al.  On using a modified Legendre-spectral method for solving singular IVPs of Lane-Emden type , 2010, Comput. Math. Appl..

[22]  Maslina Darus,et al.  Subordination and superordination for univalent solutions for fractional differential equations , 2008 .

[23]  H. Poincaré,et al.  Les Méthodes nouvelles de la Mécanique céleste and An Introduction to the Study of Stellar Structure , 1958 .

[24]  Ravi P. Agarwal,et al.  Singular Boundary Value Problems for Superlinear Second Order Ordinary and Delay Differential Equations , 1996 .

[25]  R. Lewandowski,et al.  Identification of parameters of the fractional rheological model of viscoelastic dampers , 2010 .

[26]  Shuqin Zhang,et al.  The Existence of a Positive Solution for a Nonlinear Fractional Differential Equation , 2000 .