A study of fractional calculus operators associated with the family of W-function

Abstract

The objective of the present work is to establish the fractional integral and derivative formula for the new generalised hypergeometirc function: incomplete $\mathbb{W}$-functions by using the generalised fractional calculus formulas involving the Appell function.  Additionally, corresponding assertions are made using the Weyl and Riemann-Liouville types of fractional integral and derivative formulas. The Yang-Yu $\mathbb{W}$-function is then specialised to present some interesting results of the primary discoveries.