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

[摘要] In this paper, we establish certain generalized fractional integral inequalities of mean and trapezoid type for $(s+1)$ -convex functions involving the $(k,s)$ -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.

[学科分类] 电力

[关键词] Mean-type inequalities;h -convex;\((s+1)\) -convex;k -conformable integral;\((k;s)\) -Riemann–Liouville fractional integral;Conformable integral;Trapezoid inequalities