Extension of the k-Beta Function Using the Two-Parameter Generalized Mittag-Leffler Function

Abstract

This paper introduces a new extension of the k-Beta function through the two-parameter generalized ML function, highlighting a crucial link between these mathematical constructs. The k-Beta function, recognized for its diverse applications, is expanded to reflect the flexibility of the generalized ML function in fractional calculus and various fields. We discuss important identities and properties of this extended k-Beta function. Our results deepen the understanding of the relationship between these special functions and offer valuable resources for researchers in mathematics and related disciplines investigating fractional processes and their applications.