New developments in fractional integral inequalities via convexity with applications

The main objective of this article is to build up a new integral equality related to Riemann Liouville fractional (RLF) operator. Based on this integral equality, we show numerous new inequalities for differentiable convex as well as concave functions which are similar to celebrated Hermite-Hadamard and Simpson's integral inequalities. The present outcomes of this paper are a unification and generalization of the comparable results in the literature on Hermite-Hadamard and Simpson's integral inequalities. Furthermore as applications in numerical analysis, we find some means, q-digamma function and modified Bessel function type inequalities.

Automated summary

The main objective of this article is to establish a new integral equality related to the Riemann Liouville fractional (RLF) operator. Based on this integral equality, the author presents numerous new inequalities for differentiable convex and concave functions, which are similar to well-known Hermite-Hadamard and Simpson's integral inequalities. The findings of this paper provide a unification and generalization of comparable results in the literature on Hermite-Hadamard and Simpson's integral inequalities. Additionally, the paper explores applications in numerical analysis, finding some new inequalities involving mean values, q-digamma functions, and modified Bessel functions.