On a Proportional Fractional Holomorphic Functions of Two Complex Variables with Respect to Another Function

The aim of this paper is to present a novel work related to a notion of proportional fractional holomorphic function on two complex variables with respect to another function as a structural extension of the classical theory of holomorphic functions on two complex variables. The Stokes and Borel–Pompeiu formulas are given as main results and a number of important consequences, including a Cauchy integral formula and a Cauchy theorem for proportional fractional holomorphic functions of two complex variables with respect to another function.