Open AccessHermite-Hadamard type inclusions via generalized Atangana-Baleanu fractional operator with application
Author(s) -
Soubhagya Kumar Sahoo,
Fahd Jarad,
Bibhakar Kodamasingh,
Artion Kashuri
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022683
Subject(s) - mathematics , differentiable function , equivalence (formal languages) , hadamard transform , type (biology) , operator (biology) , pure mathematics , fractional calculus , convex function , midpoint , identity (music) , hermite polynomials , monotonic function , regular polygon , mathematical analysis , ecology , biochemistry , chemistry , geometry , repressor , gene , transcription factor , biology , physics , acoustics
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.