Inequalities Including Fractional Integral Operators of General Riemann–Liouville for an Abstract Convex Function and Their Applications

An abstract convexity type is B−1–convexity. For B−1–convex functions, the Hermite–Hadamard inequality was previously found. Recently, however, new and more popular types of fractional integral operators have been developed. This paper’s goal is to demonstrate the Hermite–Hadamard inequality using additional, more general kinds of fractional integral operators. The generalization of the results are proven with the additional theorems. It is shown that the old fractional Hermite–Hadamard inequalities for B−1–convex functions can be obtained from the new inequalities given in this paper. Additionally, applications for each results are presented with tables and graphs. The inequalities for incomplete gamma function are proved and presented with graphs.