Abstract
In this manuscript, we elucidate essential connections associated with
the ( α , k ) − gamma and ( α , k ) − beta functions, initially
introduced by Sarikaya et al. in their work as referenced in [14].
Our investigation includes the establishment of numerous conformable
fractional integral inequalities, extending those previously established
for the k−gamma and k−beta functions. Furthermore, we
provide rigorous proofs affirming the log-convex nature of both the ( α
, k ) − gamma and ( α , k ) − beta functions.