  The main objective of this article is to present $\nu$-fractional derivative
$\mu$-differentiable functions by considering 4-parameters extended
Mittag-Leffler function (MLF). We investigate that the new $\nu$-fractional
derivative satisfies various properties of order calculus such as chain rule,
product rule, Rolle's and mean-value theorems for $\mu$-differentiable function
and its extension. Moreover, we define the generalized form of inverse property
and the fundamental theorem of calculus and the mean-value theorem for
integrals. Also, we establish a relationship with fractional integral through
truncated $\nu$-fractional integral.
