In this paper, we present some new Hermite-Hadamard-Fejér type inequality for fractional integrals for (η 1 , η 2 )-convex functions. Our results give some new error bounds for the weighted trapezoidal and weighted midpoint rules in fractional domain. The results presented here are noteworthy extensions of earlier works.

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In this paper, we study generalized definitions of left and right conformable fractional derivative and integrals. Some applications of the generalized definition are also given for the nonlinear fractional differential equations. We also establish identities associated with the left‐ and right‐hand side of Hermite–Hadamard–Fejér inequality for preinvex functions. We, then, give some new bounds for the Hermite–Hadamard–Fejér inequalities for preinvex functions using the generalized conformable fractional integrals.

In this paper, we have established the Hermite–Hadamard–Fejér inequality for fractional integrals involving preinvex functions. The results presented here provide new extensions of those given in earlier works as the weighted estimates of the left and right hand side of the Hermite–Hadamard inequalities for fractional integrals involving preinvex functions doesn’t exist previously.

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