Hermite-Hadamard type inclusions via generalized Atangana-Baleanu fractional operator with application

• Published in: AIMS mathematics Vol. 7; no. 7; pp. 12303 - 12321
• Main Authors: Sahoo, Soubhagya Kumar, Jarad, Fahd, Kodamasingh, Bibhakar, Kashuri, Artion
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2022
• Subjects: atangana-baleanu fractional integral operators; convex functions; hermite-hadamard inequality; jensen's inequality; young inequality
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2022683

Defining 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 $ \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.