# Variational principle and its fractal approximate solution for fractal Lane-Emden equation

Variational principle and its fractal approximate solution for fractal Lane-Emden equation The purpose of this paper is to describe the Lane–Emden equation by the fractal derivative and establish its variational principle by using the semi-inverse method. The variational principle is helpful to research the structure of the solution. The approximate analytical solution of the fractal Lane–Emden equation is obtained by the variational iteration method. The example illustrates that the suggested scheme is efficient and accurate for fractal models.Design/methodology/approachThe author establishes the variational principle for fractal Lane–Emden equation, and its approximate analytical solution is obtained by the variational iteration method.FindingsThe variational iteration method is very fascinating in solving fractal differential equation.Originality/valueThe author first proposes the variational iteration method for solving fractal differential equation. The example shows the efficiency and accuracy of the proposed method. The variational iteration method is valid for other nonlinear fractal models as well. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat & Fluid Flow Emerald Publishing

# Variational principle and its fractal approximate solution for fractal Lane-Emden equation

, Volume 31 (7): 9 – Jul 6, 2021
9 pages      /lp/emerald-publishing/variational-principle-and-its-fractal-approximate-solution-for-fractal-q08Mo5BEcZ
Publisher
Emerald Publishing
ISSN
0961-5539
DOI
10.1108/hff-09-2020-0552
Publisher site
See Article on Publisher Site

### Abstract

The purpose of this paper is to describe the Lane–Emden equation by the fractal derivative and establish its variational principle by using the semi-inverse method. The variational principle is helpful to research the structure of the solution. The approximate analytical solution of the fractal Lane–Emden equation is obtained by the variational iteration method. The example illustrates that the suggested scheme is efficient and accurate for fractal models.Design/methodology/approachThe author establishes the variational principle for fractal Lane–Emden equation, and its approximate analytical solution is obtained by the variational iteration method.FindingsThe variational iteration method is very fascinating in solving fractal differential equation.Originality/valueThe author first proposes the variational iteration method for solving fractal differential equation. The example shows the efficiency and accuracy of the proposed method. The variational iteration method is valid for other nonlinear fractal models as well.

### Journal

International Journal of Numerical Methods for Heat & Fluid FlowEmerald Publishing

Published: Jul 6, 2021

Keywords: Fractal Lane–Emden equation; Two-scale transform method; Variational principle; Variational iteration method

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