Extended Hyperbolic Function and its Properties

Aim of this paper is to introduce extended hyperbolic function by using a modified extension of beta function [12] and to establish new properties like integral representation, Mellin transform and many more. Furthermore, we apply Prabhakar fractional integral operator, Caputo-Fabrizio operator and Atangana-Baleanu operator on it. Other than this, we present a graphical representation of the extended hyperbolic function with different values of alpha also a graphical comparison between Caputo-Fabrizio operator and Atangana-Baleanu operator of hyperbolic function for different values of r.