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In this article, we study an unsteady flow of an anomalous Oldroyd-B fluid confined between two infinite parallel plates subject to no-slip condition at boundary. The flow is induced by a linear acceleration of the lower plate in its own plane. A standard Galerkin finite element method is adopted to construct an approximate solution blended with a finite difference approximation for Caputo fractional time derivatives. The convergence of the proposed numerical scheme is substantiated, and errordoi:10.1186/s13662-016-0961-9 fatcat:jv7pkxkm55hefbmbeq6yv4txqy