Refinements of some fractional integral inequalities involving extended convex functions and fractional Caputo derivatives
Abstract This article examines famous fractional Hermite–Hadamard integral inequalities through the applications of fractional Caputo derivatives and extended convex functions. We develop modifications involving two known classical fractional extended versions of the Hermite–Hadamard type inequaliti...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-02-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-025-03259-w |
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| _version_ | 1823861441152679936 |
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| author | Muhammad Imran Shahid Mubeen Aziz Khan Thabet Abdeljawad |
| author_facet | Muhammad Imran Shahid Mubeen Aziz Khan Thabet Abdeljawad |
| author_sort | Muhammad Imran |
| collection | DOAJ |
| description | Abstract This article examines famous fractional Hermite–Hadamard integral inequalities through the applications of fractional Caputo derivatives and extended convex functions. We develop modifications involving two known classical fractional extended versions of the Hermite–Hadamard type inequalities for the convex function extensions. We also obtain the refinements of some inequalities like Fejér–Hadamard, trapezoidal, and midpoint type for two extended convex functions by applying the Caputo fractional derivative identities. The presented results yield both generalizations and improvements upon previously established inequalities. |
| format | Article |
| id | doaj-art-00ea980c9b2f413585f975711539db12 |
| institution | Kabale University |
| issn | 1029-242X |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj-art-00ea980c9b2f413585f975711539db122025-02-09T12:59:33ZengSpringerOpenJournal of Inequalities and Applications1029-242X2025-02-012025111910.1186/s13660-025-03259-wRefinements of some fractional integral inequalities involving extended convex functions and fractional Caputo derivativesMuhammad Imran0Shahid Mubeen1Aziz Khan2Thabet Abdeljawad3Department of Mathematics, University of SargodhaDepartment of Mathematics, University of SargodhaDepartment of Mathematics and Science, Prince Sultan UniversityDepartment of Mathematics and Science, Prince Sultan UniversityAbstract This article examines famous fractional Hermite–Hadamard integral inequalities through the applications of fractional Caputo derivatives and extended convex functions. We develop modifications involving two known classical fractional extended versions of the Hermite–Hadamard type inequalities for the convex function extensions. We also obtain the refinements of some inequalities like Fejér–Hadamard, trapezoidal, and midpoint type for two extended convex functions by applying the Caputo fractional derivative identities. The presented results yield both generalizations and improvements upon previously established inequalities.https://doi.org/10.1186/s13660-025-03259-wExponential trigonometric convex functionslog-convex functionsCaputo fractional derivativesFractional integral inequalities |
| spellingShingle | Muhammad Imran Shahid Mubeen Aziz Khan Thabet Abdeljawad Refinements of some fractional integral inequalities involving extended convex functions and fractional Caputo derivatives Journal of Inequalities and Applications Exponential trigonometric convex functions log-convex functions Caputo fractional derivatives Fractional integral inequalities |
| title | Refinements of some fractional integral inequalities involving extended convex functions and fractional Caputo derivatives |
| title_full | Refinements of some fractional integral inequalities involving extended convex functions and fractional Caputo derivatives |
| title_fullStr | Refinements of some fractional integral inequalities involving extended convex functions and fractional Caputo derivatives |
| title_full_unstemmed | Refinements of some fractional integral inequalities involving extended convex functions and fractional Caputo derivatives |
| title_short | Refinements of some fractional integral inequalities involving extended convex functions and fractional Caputo derivatives |
| title_sort | refinements of some fractional integral inequalities involving extended convex functions and fractional caputo derivatives |
| topic | Exponential trigonometric convex functions log-convex functions Caputo fractional derivatives Fractional integral inequalities |
| url | https://doi.org/10.1186/s13660-025-03259-w |
| work_keys_str_mv | AT muhammadimran refinementsofsomefractionalintegralinequalitiesinvolvingextendedconvexfunctionsandfractionalcaputoderivatives AT shahidmubeen refinementsofsomefractionalintegralinequalitiesinvolvingextendedconvexfunctionsandfractionalcaputoderivatives AT azizkhan refinementsofsomefractionalintegralinequalitiesinvolvingextendedconvexfunctionsandfractionalcaputoderivatives AT thabetabdeljawad refinementsofsomefractionalintegralinequalitiesinvolvingextendedconvexfunctionsandfractionalcaputoderivatives |