The Jacobian matrix algorithm is often used to calculate the Lyapunov exponents of the chaotic systems. This study extends the algorithm to discrete fractional cases. The tangent maps with memory effect are presented. The Lyapunov exponents of one and two dimensional fractional logistic maps are calculated. The positive ones are used to distinguish the chaotic areas of the maps. (C) 2014 Elsevier B.V. All rights reserved.