Fractional Hermite–Hadamard-Type Inequalities for Differentiable Preinvex Mappings and Applications to Modified Bessel and q-Digamma Functions

Author:

Tariq Muhammad1ORCID,Ahmad Hijaz23ORCID,Shaikh Asif Ali14ORCID,Ntouyas Sotiris K.5ORCID,Hınçal Evren4,Qureshi Sania124ORCID

Affiliation:

1. Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan

2. Department of Computer Science and Mathematics, Lebanese American University, Beirut 1102-2801, Lebanon

3. Operational Research Center in Healthcare, Near East University, Mersin 99138, Turkey

4. Department of Mathematics, Near East University, Mersin 99138, Turkey

5. Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece

Abstract

The theory of convexity pertaining to fractional calculus is a well-established concept that has attracted significant attention in mathematics and various scientific disciplines for over a century. In the realm of applied mathematics, convexity, particularly in relation to fractional analysis, finds extensive and remarkable applications. In this manuscript, we establish new fractional identities. Employing these identities, some extensions of the fractional H-H type inequality via generalized preinvexities are explored. Finally, we discuss some applications to the q-digamma and Bessel functions via the established results. We believe that the methodologies and approaches presented in this work will intrigue and spark the researcher’s interest even more.

Publisher

MDPI AG

Subject

Applied Mathematics,Computational Mathematics,General Engineering

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