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In this paper, we compare solutions of q-order fractional differential equations of Caputo type for q near 1 with solutions of the corresponding 1-order ordinary differential equations. By establishing the explicit lower and upper bounds of Mittag-Leffler functions, we obtain the effective convergence results. It is shown that the limit cases q → 1 + and q → 1 -are different. A simple illustrative example is also presented.doi:10.1186/s13662-019-2086-4 fatcat:zcaqy3filjanbbmtmx43qkvbo4