Function (biology)

Galerkin method

Algorithm

Residual

Truncation error

Biology

Power series

Applied mathematics

Convergence (economics)

Economics

Method of mean weighted residuals

Taylor series

Evolutionary biology

Paleontology

Thermodynamics

Physics

Finite element method

Mathematics

Laplace transform

Inverse Laplace transform

Green's function for the three-variable Laplace equation

Mathematical analysis

Series (stratigraphy)

Economic growth

Fractional calculus

Laplace transform applied to differential equations

Alexandria Engineering Journal

In this paper, a reliable analytical solution for a class of the fractional Lane-Emden equations is prepared. A new technique, the Laplace-residual power series, is employed to construct a series solution to the equations. The concepts of Laplace transform, fractional Laurent series, fractional power series, and residual error function are the primary tools of the used method. We present a series solution of a class of Lane-Emden equations with fast convergence and easy finding of the coefficients using the concept of limit at infinity. To demonstrate the efficiency and trustworthiness of the Laplace- residual power series method, we consider four interesting examples to get approximate and exact solutions. We compare the obtained results with the actual values to show the precision of the suggested method.

Reliable solutions to fractional Lane-Emden equations via Laplace transform and residual error function