  This paper presents a reformulation of the Leibniz product rule as a finite
sum that expresses the fractional derivative of the product of two
differentiable functions. This paper then proves the cases for when the product
consists of an arbitrary differentiable function and a Sheffer sequence , and
the case for when the product consists of an arbitrary differentiable function
and a confluent hypergeometric limiting function with a positive integer order.
Finally, this paper provides example expressions for certain Sheffer sequences:
any Apell sequence, the falling factorial, the rising factorial, the
exponential polynomial, and the Associated Laguerre polynomial.
