Analytical study of fractional Bratu-type equation arising in electro-spun organic nanofibers elaboration

In this article, we present a hybrid analytical scheme, namely, homotopy perturbation transform method to achieve the solutions of the non-linear Bratu-type problem with fractional order derivatives. The Caputo type fractional derivatives are considered in the present article. He's polynomial is used to tackle the nonlinearity which arise in our considered problem. Using the initial conditions, the numerical solutions of the problem are computed. The numerical procedure reveals that only a few iterations are needed for better approximation of the solutions, which illustrates the effectiveness and reliability of the method. Effects of fractional order derivatives on the solutions for various particular cases are depicted through graphs. (C) 2019 Published by Elsevier B.V.