Fractional integral identity, estimation of its bounds and some applications to trapezoidal quadrature rule

The aim of this paper is to introduce a new extension of preinvexity called exponentially (m, ω1, ω2, h1, h2)–preinvexity. Some new integral inequalities of Hermite–Hadamard type for exponentially (m, ω1, ω2, h1, h2)–preinvex functions via Riemann–Liouville fractional integral are established. Also, some new estimates with respect to trapezium-type integral inequalities for exponentially (m, ω1, ω2, h1, h2)– preinvex functions via general fractional integrals are obtained. We show that the class of exponentially (m, ω1, ω2, h1, h2)–preinvex functions includes several other classes of preinvex functions. We shown by two basic examples the efficiency of the obtained inequalities on the base of comparing those with the other corresponding existing ones. At the end, some new error estimates for trapezoidal quadrature formula are provided as well. This results may stimulate further research in different areas of pure and applied sciences.