An Extended k-type Hypergeometric Functions

Abstract: Hypergeometric functions and their generalizations play an important r^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing (presumably new) extended $k-$type hypergeometric function ${2}f{1}^{k}[a, b; c; \omega; z]$ and study various properties including integral representations, differential formulas and fractional integral and derivative formula.