Abstract
In this work, a general class of multi-order fractional differential equations of Lane-Emden type is considered. Here, an assumed approximate solution is substituted into a slightly perturbed form of the general class and the resulting equation is collocated at equally spaced interior points to give a system of linear algebraic equations which are then solved by suitable computer software; Maple 18.
Highlights
Perturbation Collocation Method is a technique of numerical approximation
The results reveal that the method is effective as a small number of shifted Legendre polynomials were needed to obtain a satisfactory result. [7] presented a numerical solution method for solving fractional differential equations using Bernstein polynomials
According to [13], Lane-Emden type of differential equation is used to describe a variety of phenomena in physics and astrophysics, including isothermal gas spheres and thermionic currents and determining their numerical solutions is very challenging because of the singularity behaviours at the point of origin
Summary
Perturbation Collocation Method is a technique of numerical approximation It has been described as a very useful tool for solving differential and integro-differential equations of different kinds [1, 2, 3]. [4, 5] proposed Variational Iteration Method (VIM) and used the method to solve multi-order fractional integro-differential equations and singular IVPs of LaneEmden type respectively. Their results showed that the method is an accurate one that yields the exact solution within a few iterations. We are concerned with multi-order fractional differential equations of Lane-Emden type and their solutions by perturbation collocation method. The general form of the singular multi-order fractional differential equation is given as n i=0
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