Numerical solution of a fractional differential equation arising in optics

The aim of the article is to apply an efficient semi-analytical algorithm for the approximate solution of a fractional differential equation that governs ray tracing through the crystalline lens. A Laplace decomposition method (LDM) is implemented for the solution of the nonlinear ray equation of fractional order that is complemented with initial conditions. This method is a combination of Laplace transform and a decomposition method. The nonlinear term is decomposed and a recursive algorithm is constructed for the determination of the infinite series solution. Numerical tests are conducted, and the results confirm that this strategy converges rapidly with high accuracy using only few iterates of the recursive scheme.