Abstract
In this paper, we establish a generalize weighted fractional derivative operator involving Mittag-Leffler function in its kernel. This new operator generalizes some well known operators like the Prabhakar fractional derivative. Some significant characteristics of the newly established operator are studied. The weighted fractional derivative and inverse integral of extended hypergeometric function are evaluated. The weighted Laplace transform of fractional derivative operator is obtained. The relationship between weighted and classical Laplace is proved by presenting some examples. The solution of the fractional kinetic differintegral equation is expressed as a series involving the Mittag-Leffler function. The growth model with graphical representation is provided as applications in engineering.
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