Some new notions of fractional Hermite-Hadamard type inequalities involving applications to the physical sciences

Volume 33, Issue 1, pp 27--41 http://dx.doi.org/10.22436/jmcs.033.01.03

Publication Date: November 16, 2023 Submission Date: July 24, 2023 Revision Date: August 26, 2023 Accteptance Date: October 14, 2023

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Authors

H. Ahmad - Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, 42210 , Saudi Arabia. - Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey. - Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon. R. B. Khokhar - Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan. M. Suleman - Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan. M. Tariq - Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan. S. K. Ntouyas - Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece. J. Tariboon - Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand.

Abstract

The term convexity in the frame of fractional calculus is a well-established concept that has assembled significant attention in mathematics and various scientific disciplines for over a century. It offers valuable insights and results in diverse fields, along with practical applications due to its geometric interpretation. Moreover, convexity provides researchers with powerful tools and numerical methods for addressing extensive interconnected problems. In the realm of applied mathematics, convexity, particularly in relation to fractional analysis, finds extensive and remarkable applications. In this manuscript, we construct new fractional identities for differentiable preinvex functions to strengthen the recently assigned approach even more. Then utilizing these identities, some generalizations of the Hermite-Hadamard type inequality involving generalized preinvexities in the frame of fractional integral operator, namely Riemann-Liouville (R-L) fractional integrals are explored. Finally, we examined some applications to the \(q\)-digamma and Bessel functions via the established results. We used fundamental methods to arrive at our conclusions. We anticipate the techniques and approaches addressed by this study will further pique and spark the researcher's interest.

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Keywords

• Convex function
• invex sets
• preinvex functions
• Holder's inequality
• power mean inequality

MSC

•  26A51
•  26A33
•  26D07
•  26D10
•  26D15

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