Extended Mittag-Leffler Function and truncated $ u$-fractional derivatives

The main objective of this article is to present $ u$-fractional derivative $mu$-differentiable functions by considering 4-parameters extended Mittag-Leffler function (MLF). We investigate that the new $ u$-fractional derivative satisfies various properties of order calculus such as chain rule, product rule, Rolles 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 $ u$-fractional integral.