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.