Further Hermite–Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels
This paper introduces new versions of Hermite–Hadamard, midpoint- and trapezoid-type inequalities involving fractional integral operators with exponential kernels. We explore these inequalities for differentiable convex functions and demonstrate their connections with classical integrals. This paper...
| Published in: | Fractal and Fractional |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Multidisciplinary Digital Publishing Institute (MDPI)
2024
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| Online Access: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85196880081&doi=10.3390%2ffractalfract8060345&partnerID=40&md5=43d131148d975d3f1e1c3b7b05962424 |
| Summary: | This paper introduces new versions of Hermite–Hadamard, midpoint- and trapezoid-type inequalities involving fractional integral operators with exponential kernels. We explore these inequalities for differentiable convex functions and demonstrate their connections with classical integrals. This paper validates the derived inequalities through a numerical example with graphical representations and provides some practical applications, highlighting their relevance to special means. This study presents novel results, offering new insights into classical integrals as the fractional order (Formula presented.) approaches 1, in addition to the fractional integrals we examined. © 2024 by the authors. |
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| ISSN: | 25043110 |
| DOI: | 10.3390/fractalfract8060345 |