A polynomial-based operational matrix approach to solve fractional-order Bratu-type problems

Abstract This article presents a computationally efficient numerical algorithm that relies on fractional-order Lagrange polynomials (FOLPs) for solving initial and boundary value problems involving nonlinear fractional-order Bratu equation. This Bratu equation is a core component of the fabrication process framework for electroscope nanofibers. We create an operational matrix of fractional integration using the FOLPs to tackle the relevant initial and boundary value problems. Additionally, when using the collocation approach, it is reduced to a set of algebraic equations that can be solved using Newton’s iterative method. The Caputo notion of the fractional derivative is utilized. The effectiveness and accuracy of the present strategy are then illustrated using a few numerical examples. It has been found that for accurate numerical computation, just a few terms of Lagrange’s polynomials are needed.