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Purpose The purpose of this study is to implement a newly introduced numerical scheme for the numerical solution of a class of nonlinear fractional Bratu-type boundary value problems (BVPs). Design/methodology/approach This strategy is based on a generalization of the variational iteration method (VIM). This proposed generalized VIM (GVIM) is particularly suitable for tackling BVPs. Findings This scheme yields accurate solutions for a class of nonlinear fractional Bratu-type BVPs, for which the errors are uniformly distributed across a given domain. A proof of convergence is included. The numerical results confirm that this approach overcomes the deficiency of the VIM and other methods that exist in the literature in the sense that the solution does not deteriorate as the authors move away from the initial starting point. Originality/value The method introduced is based on original research that produces new knowledge. To the best of the authors’ knowledge, this is the first time that this GVIM is applied to fractional BVPs.

Purpose The purpose of this paper is to find approximate solutions for a general class of fractional order boundary value problems that arise in engineering applications. Design/methodology/approach A newly developed semi-analytical scheme will be applied to find approximate solutions for fractional order boundary value problems. The technique is regarded as an extension of the well-established variation iteration method, which was originally proposed for initial value problems, to cover a class of boundary value problems. Findings It has been demonstrated that the method yields approximations that are extremely accurate and have uniform distributions of error throughout their domain. The numerical examples confirm the method’s validity and relatively fast convergence. Originality/value The generalized variational iteration method that is presented in this study is a novel strategy that can handle fractional boundary value problem more effectively than the classical variational iteration method, which was designed for initial value problems.