Sahoo, Soubhagya KumarJarad, FahdKodamasingh, BibhakarKashuri, Artion2024-03-122024-03-122022Sahoo, Soubhagya Kumar;...et.al. (2022). "Hermite-Hadamard type inclusions via generalized Atangana-Baleanu fractional operator with application", AIMS Mathematics, Vol.7, No.7, pp.12303-12321.24736988http://hdl.handle.net/20.500.12416/7553Defining 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 Hölder-İşcan, Jensen and Young inequality. Also, if we take the parameter ρ = 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/openAccessAtangana-Baleanu Fractional Integral OperatorsConvex FunctionsHermite-Hadamard InequalityJensen’s InequalityYoung InequalityArticle77123031232110.3934/math.2022683