Simpson’s type inequalities for η-convex functions via k-Riemann–Liouville fractional integrals

Abstract

We introduce some Simpson's type integral inequalities via k-Riemann-Liouville fractional integrals for functions whose derivatives are η-convex. These results generalize some results in the literature.

Simpson’s Integral Inequalities for Twice Differentiable Convex Functions

“…Among the several known inequalities, the most simple is Simpson's type, which has been successfully applied in several models of ordinary differential equations [18][19][20][21][22][23][24][25][26][27][28][29] and fractional differential equations [30][31][32]. Simpson's integral inequality is as follows: for any four times continuously differentiable function F: [ξ 1 , ξ 2 ] ⟶ R on (ξ 1 , ξ 2 ), Simpson's integral inequality is defined as follows:…”