In this paper, we define a new class of functions called generalized $\varphi$-convex function. Several variants of Hermite-Hadamard type fractional integral inequalities are presented. This ideas and techniques used in this paper may open new avenues of research and motivate the reader to explore the application of generalized $\varphi$-convex functions in various branches of pure and applied sciences.
This project is partially supported by the National Natural Science Foundation of China (No. 11971241).
"Fractional integral inequalities for generalized convexity." Tbilisi Math. J. 13 (3) 63 - 83, September 2020. https://doi.org/10.32513/tbilisi/1601344899