Sahoo, Soubhagya KumarJarad, FahdJarad, FahdKodamasingh, BibhakarKashuri, ArtionMatematik2024-03-122024-03-122022Sahoo, Soubhagya Kumar;...et.al. (2022). "Hermite-Hadamard type inclusions via generalized Atangana-Baleanu fractional operator with application", AIMS Mathematics, Vol.7, No.7, pp.12303-12321.2473-6988https://doi.org/10.3934/math.2022683Defining new fractional operators and employing them to establish well-known integral inequalities has been the recent trend in the theory of mathematical inequalities. To take a step forward, we present novel versions of Hermite-Hadamard type inequalities for a new fractional operator, which generalizes some well-known fractional integral operators. Moreover, a midpoint type fractional integral identity is derived for differentiable mappings, whose absolute value of the first-order derivatives are convex functions. Moreover, considering this identity as an auxiliary result, several improved inequalities are derived using some fundamental inequalities such as Holder-Iscan, Jensen and Young inequality. Also, if we take the parameter rho = 1 in most of the results, we derive new results for Atangana-Baleanu equivalence. One example related to matrices is also given as an application.eninfo:eu-repo/semantics/openAccessConvex FunctionsHermite-Hadamard InequalityAtangana-Baleanu Fractional Integral OperatorsYoung InequalityJensen'S InequalityArticle77123031232110.3934/math.20226832-s2.0-85129377262WOS:000791830800002Q1Q1