University of Tabriz Computational Methods for Differential Equations 2345-3982 7 2 2019 04 01 Accurate splitting approach to characterize the solution set of boundary layer problems 206 223 8666 EN Khosro Sayevand Faculty of Mathematical Sciences, Malayer University, P. O. Box 16846-13114, Malayer, Iran Jose Antonio Tenreiro Machado Institute of Engineering of Polytechnic of Porto, Department of Electrical Engineering, Porto, Portugal Journal Article 2018 01 26 The boundary layer (BL) is an important concept and refers to the layer of fluid in the immediate vicinity of a bounding surface where the effects of viscosity are significant. This paper studies singularly perturbed fractional differential equations where the fractional derivatives are defined in the Caputo sense. The solution of such equations, with appropriate boundary conditions, displays BL behavior. The solution out of the BL is estimated by the solution of the reduced problem and the layer solution is approximated by means of a modified truncated Chebyshev series. The coefficients of the truncated series are evaluated using a novel operational matrix technique. Moreover, the stability and the error analysis of the proposed method are analyzed. Several examples illustrate the validity and applicability of the method. https://cmde.tabrizu.ac.ir/article_8666_d7b613d4c647b73430148d5432da5c39.pdf