Exploring Triple-k And Penta- k Extensions Of Some Generalized Mittag-Leffler Functions And Their Riemann-Liouville k -Fractional Integrals

Abstract

This study presents a novel extension of the generalized classical beta function. Additionally, we introduce a triple  extension and a penta extension of the generalized classical Mittag-Leffler (ML) function, building upon the extended beta function. These new forms significantly broaden the scope of ML functions. Moreover, we derive the Riemann-Liouville (RL) fractional integrals (FIs) of some functions that incorporate these extended ML functions, further expanding their applications.