On the numerical computation of the Mittag-Leffler function

•An algorithm is developed to approximate Eα,1(-tα)Eα,1(-tα).•Errors are clearly lower than those of usual asymptotic approximations.•The algorithm runs in average 2277 times faster than computing function Eα,1Eα,1.

Recently simple limiting functions establishing upper and lower bounds on the Mittag-Leffler function were found. This paper follows those expressions to design an efficient algorithm for the approximate calculation of expressions usual in fractional-order control systems. The numerical experiments demonstrate the superior efficiency of the proposed method.