Inequalities Involving Special Functions in Conformable Fractional Integrals

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.