Abstract
In this work, we study the fractional order Lane-Emden differential equations by using the reproducing kernel method. The exact solution is shown in the form of a series in the reproducing kernel Hilbert space. Some numerical examples are given in order to demonstrate the accuracy of the present method. The results obtained from the method are compared with the exact solutions and another method. The obtained numerical results are better than the ones provided by the collocation method. Results of numerical examples show that the presented method is simple, effective, and easy to use.
Highlights
1 Introduction The fractional differential equations of various types plays important roles and tools in mathematics and in physics, control systems, dynamical systems and engineering to create the mathematical modeling of many physical phenomena
The Lane-Emden differential equations are important for mathematical modeling [ ]
Lane-Emden differential equations are singular initial value problems relating to second order differential equations (ODEs) utilized to model successfully several real world phe
Summary
The fractional differential equations of various types plays important roles and tools in mathematics and in physics, control systems, dynamical systems and engineering to create the mathematical modeling of many physical phenomena. The Lane-Emden differential equations are important for mathematical modeling [ ]. The goal of our manuscript is to research the effectiveness of reproducing kernel method (RKM) to solve fractional differential equations of Lane-Emden type. Lane-Emden differential equations are singular initial value problems relating to second order differential equations (ODEs) utilized to model successfully several real world phe-. Taking into account the memory effects are better described within the fractional derivatives, the fractional Lane-Emden equations are extracting hidden aspects for the complex phenomena they described in various field of the applied mathematics, mathematical physics, and astrophysics [ , ]. We recall that a general solution technique for fractional differential equations has not yet been constituted. The solution of ( )-( ) is presented in the reproducing kernel Hilbert space o [ , ].
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