  The two-parametric Mittag-Leffler function (MLF), $E_{\alpha,\beta}$, is
fundamental to the study and simulation of fractional differential and integral
equations. However, these functions are computationally expensive and their
numerical implementations are challenging. In this paper, we present a unified
framework for developing global rational approximants of
$E_{\alpha,\beta}(-x)$, $x>0$, with $\{ (\alpha,\beta): 0 < \alpha \leq 1,
\beta \geq \alpha, (\alpha,\beta) \ne (1,1) \}$. This framework is based on the
series definition and the asymptotic expansion at infinity. In particular, we
develop three types of fourth-order global rational approximations and discuss
how they could be used to approximate the inverse function. Unlike existing
approximations which are either limited to MLF of one parameter or of low
accuracy for the two-parametric MLF, our rational approximants are of fourth
order accuracy and have low percentage error globally. For efficient
utilization, we study the partial fraction decomposition and use them to
approximate the two-parametric MLF with a matrix argument which arise in the
solutions of fractional evolution differential and integral equations.
