Certain mean-type fractional integral inequalities via different convexities with applications

Abstract

Abstract In this paper, we establish certain generalized fractional integral inequalities of mean and trapezoid type for ( s + 1 ) $(s+1)$ -convex functions involving the ( k , s ) $(k,s)$ -Riemann–Liouville integrals. Moreover, we develop such integral inequalities for h-convex functions involving the k-conformable fractional integrals. The legitimacy of the derived results is demonstrated by plotting graphs. As applications of the derived inequalities, we obtain the classical Hermite–Hadamard and trapezoid inequalities.

Keywords

• Mean-type inequalities
• h-convex; ( s + 1 ) $(s+1)$ -convex
• k-conformable integral
• ( k , s ) $(k,s)$ -Riemann–Liouville fractional integral
• Conformable integral
• Trapezoid inequalities