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

AM > Vol.3 No.8, August 2012

Applied Mathematics

Volume 3, Issue 8 (August 2012)

ISSN Print: 2152-7385 ISSN Online: 2152-7393

Google-based Impact Factor: 0.58 Citations

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

HTML

Download as PDF (Size: 151KB) PP. 851-856

DOI: 10.4236/am.2012.38126 6,276 Downloads 11,460 Views Citations

Author(s)

Mohammed S. Mechee, Norazak Senu

Affiliation(s)

Department of Mathematics, Universiti Putra Malaysia 43400 UPM Serdang,Selangor, Malaysia.
Institute of Mathematical Sciences, University of Malaya 50603 Kuala Lumpur, Malaysia.

ABSTRACT

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.

KEYWORDS

Fractional Calculus; Fractional Differential Equation; Lane-Emden Equation; Numerical Collection Method

Share and Cite:

M. Mechee and N. Senu, "Numerical Study of Fractional Differential Equations of Lane-Emden Type by Method of Collocation," Applied Mathematics, Vol. 3 No. 8, 2012, pp. 851-856. doi: 10.4236/am.2012.38126.

Cited by

[1]	FMNSICS: Fractional Meyer neuro-swarm intelligent computing solver for nonlinear fractional Lane–Emden systems
	Neural Computing and …, 2022

[2]	An efficient hybrid computational technique for the time dependent Lane-Emden equation of arbitrary order
	Journal of Ocean Engineering and …, 2022

[3]	Numerical simulation of variable-order fractional differential equation of nonlinear Lane–Emden type appearing in astrophysics
	International Journal of Nonlinear Sciences and …, 2022

[4]	Approximate Analytical Solution of Fractional Lane-Emden Equation by Mittag-Leffler Function Method
	Journal of the Nigerian Society …, 2022

[5]	Generalized Euler and Runge-Kutta methods for solving classes of fractional ordinary differential equations
	International Journal of Nonlinear …, 2022

[6]	Analytical Solutions of a Class of Fractional Lane–Emden Equation: A Power Series Method
	International Journal of Applied and Computational …, 2022

[7]	New analytical method of solution to a nonlinear singular fractional Lane–Emden type equation
	AIMS Mathematics, 2022

[8]	On a fractional problem of Lane–Emden type: Ulam type stabilities and numerical behaviors
	Advances in …, 2021

[9]	Stability of solutions for two classes of fractional differential equations of Lane-Emden type
	2021

[10]	Wavelet Theory: Applications of the Wavelet
	2021

[11]	A novel design of fractional Meyer wavelet neural networks with application to the nonlinear singular fractional Lane-Emden systems
	2021

[12]	An anti-periodic singular fractional differential problem of Lane-Emden type
	2021

[13]	Sumudu transform for solving some classes of fractional differential equations
	2021

[14]	The Pantograph equation with nonlocal conditions via Kantugampola fractional derivative
	2021

[15]	Caputo-Hadamard approach applications: solvability for an integro-differential problem of Lane and Emden type
	2021

[16]	Solvability for a class of nonlocal singular fractional differential equations of Lane Emden type
	2021

[17]	Numerical methods for solving Lane-Emden type differential equations by operational matrix of fractional derivative of modified generalized Laguerre …
	2021

[18]	A novel Chebyshev neural network approach for solving singular arbitrary order Lane-Emden equation arising in astrophysics
	2020

[19]	A nonlocal multi‐point singular fractional integro‐differential problem of Lane–Emden type
	2020

[20]	Application of fractional calculus on a new differential problem of duffing type
	2020

[21]	Application of MHPM for Solving Semi-Linear Fractional Differential Equations
	2020

[22]	Perturbed Collocation Method For Solving Singular Multi-order Fractional Differential Equations of Lane-Emden Type
	2020

[23]	A single layer fractional orthogonal neural network for solving various types of Lane–Emden equation
	2020

[24]	Generalized Bessel polynomial for multi-order fractional differential equations
	2020

[25]	Fractional Singular Differential Systems of Lane–Emden Type: Existence and Uniqueness of Solutions
	2020

[26]	A generalized sequential problem of Lane-Emden type via fractional calculus
	… Journal of Pure and Applied Analysis, 2020

[27]	ULAM-HYERS-RASSIAS STABILITY OF FRACTIONAL LANE-EMDEN EQUATIONS.
	2019

[28]	A TWO-PARAMETER SINGULAR FRACTIONAL DIFFERENTIAL EQUATION OF LANE EMDEN TYPE
	2019

[29]	Simulation of nonlinear fractional dynamics arising in the modeling of cognitive decision making using a new fractional neural network
	Mathematical Methods in the Applied Sciences, 2019

[30]	A novel design of fractional Mayer wavelet neural networks with application to the nonlinear singular fractional Lane-Emden systems
	2019

[31]	Series solutions for the Laguerre and Lane-Emden fractional differential equations in the sense of conformable fractional derivative
	2019

[32]	A class of nonlinear singular differential equations
	2019

[33]	Haar Wavelet Technique for Solving Fractional Differential Equations with An Application
	2019

[34]	Polynomial Least Squares Method for Fractional Lane–Emden Equations
	2019

[35]	Approximate Solution of Fractional Order Lane–Emden Type Differential Equation by Orthonormal Bernoulli's Polynomials
	2019

[36]	Numerical study of singular fractional Lane–Emden type equations arising in astrophysics
	2019

[37]	A Lane Emden Type Problem Involving Caputo Derivative and Riemann-Liouville Integral
	2019

[38]	ULAM-HYERS-RASSIAS STABILITY OF FRACTIONAL LANE-EMDEN EQUATIONSS
	2019

[39]	Ulam-Hyers-Rassias Stability of Fractional Lane-Emden Equations
	2019

[40]	An Efficient Numerical Method For Solving Nonlinear Astrophysics Equations of Arbitrary Order
	2018

[41]	The Combined Reproducing Kernel Method and Taylor Series for Handling Fractional Differential Equations
	2018

[42]	The Lane-Emden fractional homogeneous differential equation
	2017

[43]	Novel orthogonal functions for solving differential equations of arbitrary order
	Tbilisi Mathematical Journal, 2017

[44]	Approximate Analytical Methods For Ordinary Differential Equations Of Fractional Order
	2017

[45]	On A Class of Fractional Differential Equations with Arbitrary Singularities
	2016

[46]	THE HIGHT ORDER LANE-EMDEN FRACTIONAL DIFFERENTIAL SYSTEM: EXISTENCE, UNIQUENESS AND ULAM TYPE STABILITIES
	2016

[47]	Chebyshev neural network model with linear and nonlinear active functions
	2016

[48]	Numerical solutions of fractional differential equations of Lane-Emden type by an accurate technique
	Advances in Difference Equations, 2015

[49]	Approximate Solutions of Fisher's Type Equations with Variable Coefficients
	Abstract and Applied Analysis, 2013

[50]	Thème
	Les glissements de terrains (Ciloc de la ville de …, 2008

[51]	Solution of Differential Equations of Emden–Fowler Type by Homotopy Analysis Method with Genetic Algorithm

Journals Menu

Follow SCIRP

	+1 323-425-8868
	customer@scirp.org
	+86 18163351462(WhatsApp)
	1655362766

	Paper Publishing WeChat

Journals Menu

Home

About SCIRP

Service

Policies