MMN-453
Existence of nonlinear Lane-Emden equation offractional order
Abstract
We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional
orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and
astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal
gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct
description of the dynamics for systems in complex media. In order to overcome this problem and describe
dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed.
One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden
equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of
Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible
model for fractal processes as compared with the usual one characterized by a single index. The contraction
mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the
problem in a Banach space.
Vol. 13 (2012), No. 1, pp. 39-52