Perturbation Theory for the Matrix Mittag-Leffler Function

This paper establishes perturbation theories for the matrix Mittag-Leffler function E-alpha,E-beta (A), where alpha > 0, beta is an element of Rand A is an element of C-nxn. We present upper bounds on ||||E-alpha,E-beta (A + Delta)- E-alpha,E-beta (A)||, larger the presented bounds are compared to ||E-alpha,E-beta (A + Delta) - E-alpha,E-beta( A)||. When alpha = beta = 1, the function reduces to the matrix exponential. We compare the presented bound when alpha = beta = 1 with an existing perturbation bound for the matrix exponential.