Ostrowski-type inequalities pertaining to Atangana–Baleanu fractional operators and applications containing special functions

Abstract

Abstract The objective of this article is to incorporate the concept of the Ostrowski inequality with the Atangana–Baleanu fractional integral operator. A novel integral identity for twice-differentiable functions is established after a rigorous investigation of several basic definitions and existing ideas related to inequalities and fractional calculus. Following that, numerous Ostrowski-type inequalities are provided based on this identity, which uses Mittag–Leffler as its kernel structure. Some specific applications, such as q-digamma functions and modified Bessel functions, are also investigated. Choosing s = 1 $s=1$ , we also analyze new results for convex functions as special cases. Our findings corroborate some well-documented inequalities.

Keywords

• Ostrowski inequality
• Convex functions
• Atangana–Baleanu fractional operator
• q-digamma functions
• Modified Bessel functions