Analytical Solution of System of Fractional-Order Lane-Emden Type Equations

Articles in Press

Document Type : Original Article

Authors

1 Adekunle Ajasin University

2 Department of Mathematical Sciences, Adekunle Ajasin University, Akungba-Akungba, Ondo State, Nigeria

Abstract

Single Lane-Emden equations model several phenomena in physics and astrophysics such as isotropic continuous media, isothermal gas spheres and the thermal behaviour of a spherical cloud of gas. Systems of Lane-Emden equations appear in the modelling of several physical problems such as pattern formation,

chemical reactions, and population evolution. In this paper, a class of systems of fractional-order Lane-Emden type equations is considered using a fractional power series method. The proposed method applies generalised Cauchy product of power series to the nonlinear terms and explicit recurrence relations for the expansion coefficients of the system of series solutions are generated. The problem considered is a fractional-order version of a system of classical Lane-Emden equations studied (jointly) by B. Muatjetjeja and C.M. Khalique (First integrals for a generalized coupled Lane-Emden system, Nonlinear Anal.

Real World Appl., 12, 2011, 1202-1212); and the one

by A.M. Wazwaz (The variational iteration method for solving systems of equations of Emden-Fowler type,

Int. J. Comput. Math., 2011, 88, 3406-3415) using different methods. The illustrative examples presented generalise many problems in the literature. The solutions obtained agree excellently with the exact solutions and several published results from other methods.

Keywords

Main Subjects

Communications in Nonlinear Analysis

Articles in Press, Accepted Manuscript
Available Online from 30 December 2023

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