Some Remarks on Estimate of Mittag-Leffler Function

Abstract EN

The estimate of Mittag-Leffler function has been widely applied in the dynamic analysis of fractional-order systems in some recently published papers.

In this paper, we show that the estimate for Mittag-Leffler function is not correct.

First, we point out the mistakes made in the estimation process of Mittag-Leffler function and provide a counterexample.

Then, we propose some sufficient conditions to guarantee that part of the estimate for Mittag-Leffler function is correct.

Meanwhile, numerical examples are given to illustrate the validity of the two newly established estimates.