Generalized k-fractional integral inequalities associated with (α,m) $(\alpha ,m)$-convex functions

Abstract

Abstract This research investigates bounds of the sum of left-sided and right-sided fractional integrals in a compact form. These bounds are established by using (α,m) $(\alpha ,m)$-convex functions. The results of this paper also have connection with some known and already published results (Dragomir and Agarwal in Appl. Math. Lett. 11(5):91–95, 1998; Farid in J. Anal. 2018, https://doi.org/10.1007/s41478-0079-4; Farid et al. in Mathematics 2018(6):248, 2018). Moreover, the investigated results are applied to the end points as well as the mid point of the domain and some interesting consequences have been obtained.

Keywords

• Convex function
• ( α , m ) $(\alpha, m)$ -convex function
• Fractional integrals
• Bounds