Ford, Neville J.Morgado, Maria L.Rebelo, Magda S.2014-06-242014-06-242014-06-14Journal of Computational and Applied Mathematics, February 2015, 275, pp. 392-4020377-042710.1016/j.cam.2014.06.013http://hdl.handle.net/10034/322216NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational and Applied Mathematics, 275, February 2015, doi: 10.1016/j.cam.2014.06.013In this paper we propose a non-polynomial collocation method for solving a class of terminal (or boundary) value problems for differential equations of fractional order α, 0 < α < 1. The approach used is based on the equivalence between a problem of this type and a Fredholm integral equation of a particular form. Taking into account the asymptotic behaviour of the solution of this problem, we propose a non-polynomial collocation method on a uniform mesh. We study the order of convergence of the proposed algorithm and a result on optimal order of convergence is obtained. In order to illustrate the theoretical results and the performance of the method we present several numerical examples.ennumerical analysiscomputational and mathematical modellingArticleJournal of Computational and Applied Mathematics