(untitled) (European Journal of Pure and Applied Mathematics, 2026)
Performing a thought study of fractional inequalities by means of convexity and fractional operators has conspicuous work in the field of analysis. The main object of this paper is to discuss the coordinated convexity, pre-invexity, and also establish fractional double integral operators (FDIO) having generalized Bessel-Maitland function as used its kernel. We develop a new generation of Hermite-Hadamard (H-H) and trapezoid-type inequalities through different types of coordinated convexities and pre-invexities with successfully implementation of newly designed fractional double integral operators. Moreover, we extract some corollaries, which are generalization of well-known inequalities for different coordinated convexities that show a strong consolidation of our main results.