Generalized Hermite–Hadamard-Type Integral Inequalities for h-Godunova–Levin Functions

*emain objective of this article is to establish generalized fractional Hermite–Hadamard and related type integral inequalities for h-Godunova–Levin convexity and h-Godunova–Levin preinvexity with extended Wright generalized Bessel function acting as kernel. Moreover, Hermite–Hadamard-type and trapezoid-type inequalities for several known convexities including Godunova–Levin function, classical convex, s-Godunova–Levin function, P-function, and s-convex function are deduced as corollaries. *ese obtained results are analyzed in the form of generalization of fractional inequalities.

Definition 7 (see [38]). Pochammer's symbol is defined for δ ∈ N as for c ∈ C and m ≥ 0, where Γ being the gamma function.
Definition 8 (see [38]). e integral representation of the gamma function is defined as for R(t) > 0.
Definition 13 (see [46]). e generalized fractional integral operators, with extended generalized Bessel-Maitland function as kernel, are defined, for μ, ], η, ρ, c, c ∈ C, In the paper, we obtain Hermite-Hadamard-and trapezoid-type inequalities using the generalized fractional integral operator with extended generalized Bessel-Maitland function as its nonsingular kernel. e structure of the paper is as follows.
In Section 2, we present Hermite-Hadamard inequalities for h-Godunova-Levin convex function using the generalized fractional operator. Section 3 is devoted to trapezoidtype inequalities related to Hermite-Hadamard inequality for h-Godunova-Levin preinvex function using the generalized fractional operator.
In our work, we have frequently used the given notations:

Hermite-Hadamard Inequalities via h-Godunova-Levin Convex Function
In this section, we establish Hermite-Hadamard inequalities for h-Godunova-Levin convex function using the generalized fractional operator as follows.

Journal of Function Spaces
Solving the integrals involved in inequality (23), we obtain For the second part of inequality, again using h-Godunova-Levin convexity of Θ, we have Addition of these inequalities gives Multiplying both sides by δ v′ J μ,ξ,m,σ,c v′,η,ρ,c (ωδ μ ; p) and integrating the resulting inequality on [0, 1] with respect to δ, we obtain Solving the integrals involved leads to Combining (24) and (29), we reach to inequality. □ Corollary 1. Choosing h(δ) � δ s in eorem 1, we obtain Hermite-Hadamard-type inequality for s-Godunova-Levin function:

Trapezoid-Type Inequalities Related to Hermite-Hadamard Inequalities for h-Godunova-Levin Preinvex Function
In this section, Wright generalized that the Bessel function is restricted to a real valued function. e trapezoid-type inequalities related to Hermite-Hadamard inequalities using fractional integral with Wright generalized Bessel function in its kernel can be obtained with the help of the following lemma.

Conclusion
In the present paper, the advanced approach of the generalized fractional version of Hermite-Hadamard-type and trapezoid-type integral inequalities for a recently introduced function, h-Godunova-Levin convex, and h-Godunova-Levin preinvex have been established by using fractional integral operator with Wright generalized Bessel function as its kernel. Convexities and its different forms have remarkable uses in many fields and is extensively worked by researchers. Since h-Godunova-Levin convex function is generalization of several known convexities, so the results have been also deduced for them in the form of corollaries.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.