FRACTIONAL INTEGRAL INEQUALITIES FOR SUPERQUADRATIC FUNCTIONS VIA ATANGANA–BALEANU’S OPERATOR WITH APPLICATIONS

Saad Ihsan Butt (), Dawood Khan (), Shilpi Jain, Georgia Irina Oros, Praveen Agarwal and Shaher Momani
Additional contact information
Saad Ihsan Butt: COMSATS University Islamabad, Lahore Campus, Pakistan
Dawood Khan: COMSATS University Islamabad, Lahore Campus, Pakistan
Shilpi Jain: Department of Mathematics, Poornima University, Jaipur 302022, India
Georgia Irina Oros: Department of Mathematics and Computer Science, Faculty of Informatics and Sciences, University of Oradea, str. Universitatii nr. 1, 410087 Oradea, Romania
Praveen Agarwal: Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, United Arab Emirates5Department of Mathematical Sciences, Saveetha School of Engineering, Chennai 602105, Tamil Nadu, India6Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India
Shaher Momani: Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, United Arab Emirates7Department of Mathematics, School of Science, The University of Jordan, Amman 11942, Jordan

FRACTALS (fractals), 2025, vol. 33, issue 08, 1-24

Abstract: In this paper, the notion of superquadraticity is used to obtain some new Fejér and Hermite–Hadamard-type inequalities by means of Atangana–Baleanu’s fractional integral operators. We determine improved versions of existing results for those superquadratic functions which are also convex. Findings from the study are verified by certain reduced results, numerical calculations and graphical depictions that takes few appropriate examples into account. The fact that the work has been improved using applications of type-1 modified Bessel functions, special means and moment of random variables by describing certain novel functions in the context of modified Bessel functions and taking uniform probability density function into consideration is another motivating aspect of the research. The research presented in this publication is new concerning the concept of superquadraticity. We are quite optimistic that this has the potential to make substantial input to encouraging further research.

Keywords: Superquadratic Functions; Hermite–Hadamard’s Inequality; Atangana–Baleanu’s Fractional Integral Operator; Fejér’s Inequality; Uniform Probability Density Function; Type-1 Modified Bessel Function (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25400687

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