Generalized proportional fractional integral Hermite–Hadamard’s inequalities

Abstract The theory of fractional integral inequalities plays an intrinsic role in approximation theory also it has been a key in establishing the uniqueness of solutions for some fractional differential equations. Fractional calculus has been found to be the best for modeling physical and engineering processes. More precisely, the proportional fractional operators are one of the recent important notions of fractional calculus. Our aim in this research paper is developing some novel ways of fractional integral Hermite–Hadamard inequalities in the frame of a proportional fractional integral with respect to another strictly increasing continuous function. The considered fractional integral is applied to establish some new fractional integral Hermite–Hadamard-type inequalities. Moreover, we present some special cases throughout discussing this work.