On the solutions of the fractional Bratu’s problem

Abstract

The ultimate aim of the article is to apply an efficient semi-analytical method for the approximate solution of the fractional differential equations of Bratu–type. A Laplace Decomposition Method (LDM), which is a combination of Laplace transform and a Decomposition Method, is implemented for the nonlinear fractional Bratu problem that is complemented with initial and boundary conditions. The nonlinear term is decomposed and a recursive algorithm is composed for the determination of the proposed infinite series solution. A patching strategy, based on domain decomposition, is suggested to overcome a deficiency of the LDM. Some examples are selected to explicate the effectiveness and simplicity of the proposed technique. The results assure that this scheme is speedily convergent and quite accurate by which it approximates the solution using only few iterates of its iterative scheme.