<p>The Mittag-Leffler fractional derivative operator, whose kernel consists of a combination of the exponential law and the power law, has been usefully used in applications of fractional calculus. In this paper, we suggest a two-parameter Mittag-Leffler type fractional derivative model. The new definition generalizes the Mittag-Leffler fractional derivative with a rich variety of behaviors for derivatives as it introduces a fractional derivative with respect to two orders. We formulate the corresponding fractional integral. Then, we present a singular kernel extension of the proposed two-parameter Mittag-Leffler type fractional derivative. Moreover, we discuss some features and relationships of the proposed operators and provide solutions for some initial value problems involving the studied fractional derivatives. Next, we depict the dynamic behavior of a nonlinear model involving the proposed extended Mittag-Leffler type fractional derivative through numerical simulations. The benefit of the extended version is that it can provide useful insights into the modeling problem so that it overcomes the drawbacks of the non-singular kernel version.</p>