Some new notions of fractional HermiteHadamard type inequalities involving applications to the physical sciences
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 wellestablished 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 HermiteHadamard type inequality involving generalized preinvexities in the frame of fractional integral operator, namely RiemannLiouville (RL) 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.
Share and Cite
ISRP Style
H. Ahmad, R. B. Khokhar, M. Suleman, M. Tariq, S. K. Ntouyas, J. Tariboon, Some new notions of fractional HermiteHadamard type inequalities involving applications to the physical sciences, Journal of Mathematics and Computer Science, 33 (2024), no. 1, 2741
AMA Style
Ahmad H., Khokhar R. B., Suleman M., Tariq M., Ntouyas S. K., Tariboon J., Some new notions of fractional HermiteHadamard type inequalities involving applications to the physical sciences. J Math Comput SCIJM. (2024); 33(1):2741
Chicago/Turabian Style
Ahmad, H., Khokhar, R. B., Suleman, M., Tariq, M., Ntouyas, S. K., Tariboon, J.. "Some new notions of fractional HermiteHadamard type inequalities involving applications to the physical sciences." Journal of Mathematics and Computer Science, 33, no. 1 (2024): 2741
Keywords
 Convex function
 invex sets
 preinvex functions
 Holder's inequality
 power mean inequality
MSC
 26A51
 26A33
 26D07
 26D10
 26D15
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