A Study on Harmonic Univalent Function with $(p,q)$-Calculus and introducing $(p,q)$-Possion Distribution Series

Abstract

Looking at the history of fractional derivatives, it can be clearly seen that various generalizations have been presented for it regularly by researchers. Perhaps, in the meantime, the derivative of the  $q$-fraction has received more attention due to the provision of discrete space and the entry of the computer into the computing scene. But recently, a new generalization has been presented for the  $q$-derivative, namely $(p,q)$-derivative. In this research, we intend to define the $(p,q)$-Poisson distribution of harmonic functions by using $(p,q)$-derivatives. By that, we will check the conditions of Poisson distribution for two subclasses of harmonic univalent functions.