| Summary: | In this paper, the authors analyse and study some recent publications about integral inequalities related to generalized convex functions of several variables and the use of extended fractional integrals. In particular, they establish a new Hermite–Hadamard inequality for generalized coordinate <inline-formula><math display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>-convex functions via an extension of the Riemann–Liouville fractional integral. Furthermore, an interesting identity for functions with two variables is obtained, and with the use of it, some new extensions of trapezium-type inequalities using Raina’s special function via generalized coordinate <inline-formula><math display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>-convex functions are developed. Various special cases have been studied. At the end, a brief conclusion is given as well.
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