Research Article Fractional Integral Inequalities of Hermite–Hadamard Type for Differentiable Generalized h-Convex Functions Yingxia Yang, 1 Muhammad Shoaib Saleem , 2 Mamoona Ghafoor, 2 and Muhammad Imran Qureshi 3 1 School of Mathematics, Yunnan Normal University, Kunming 650500, China 2 Department of Mathematics, University of Okara, Okara 56300, Pakistan 3 Department of Mathematics, COMSATS University Islamabad, Vehari 61100, Pakistan Correspondence should be addressed to Muhammad Shoaib Saleem; shaby455@yahoo.com Received 17 March 2020; Accepted 19 May 2020; Published 25 June 2020 Academic Editor: Ming-Sheng Liu Copyright©2020YingxiaYangetal.isisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In the present paper, some fractional integral inequalities of Hermite–Hadamard type for functions whose derivatives are generalized h-convexareestablished.Moreover,severalparticularcasesarealsodiscussedwhichcanbededucedfromourresults. Asspecialcases,onecanobtainseveralnewversionsoftheresultsofgeneralized h-convexityforothervariousgeneralizationsof convex functions. 1.Introduction e theory of inequalities is in process of continuous de- velopmentstate,andinequalitieshavebecomeveryeffectual andpotenttoolsforanalyzingalargenumberofproblemsin different branches of mathematics. In last decades, the theoryofinequalitieshasdrawntheattentionofmostofthe researchers,motivatednewresearchdirections,andaffected several features of mathematical analysis and applications [1–4]. Among a variety of inequalities, some inequalities such as Jensen, Hilbert, Hadamard, Hardy, Poincare, Sobolev, Opial, and Fej´ er have made a significant influence on numerous branches of mathematics [5–8]. One good strategy for investigating any convexity is first to discuss maininequalitiessuchasHermite–HadamardandFej´ erand then to derive fractional integral inequalities for this. e fractionalinequalitiesforconvexfunctionarealsoimportant to calculate different means. So, it is always interesting to develop fractional integral inequalities for some generalized convexity. For recent results concerning fractional Hermi- te–Hadamard inequalities and for different generalizations of convexity, see [9–11] and references therein. In 2019, some new inequalities based on harmonic log- convex functions have been studied by Baloch et al. in [12]. In the same year, Sarikaya and Alp [13] studied the Hermite–Hadamard–Fej´ er type integral inequalities for generalized convex functions via local fractional integrals. Kwun et al. [14] studied generalized Riemann–Liouville k-fractional integrals associated with Ostrowski-type in- equalities and error bounds of Hadamard inequalities. In [15], Kang et al. studied Hadamard and Fej´ er–Hadamard inequalities for extended generalized fractional integrals involvingspecialfunctions.In[15], (h, m)-convexfunctions and associated fractional Hadamard and Fej´ er–Hadamard inequalities via an extended generalized Mittag–Leffler function were studied. Simpson’s type inequalities for strongly (s, m)− convex functions in the second sense has been studied in [16] by Kermausuor. In the present paper, we aim to study some Hermi- te–Hadamard-type fractional integral inequalities for functions whose derivatives are generalized h-convex. Our results can be considered as generalization of many existing resultsasmanyexistingresultscanbeobtaineddirectlyfrom our results. Hindawi Journal of Mathematics Volume 2020, Article ID 2301606, 13 pages https://doi.org/10.1155/2020/2301606