{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:23:56Z","timestamp":1760145836185,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T00:00:00Z","timestamp":1726012800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Taif University, Saudi Arabia","award":["TU-DSPP-2024-87"],"award-info":[{"award-number":["TU-DSPP-2024-87"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper aims to introduce a new fractional extension of the interval Hermite\u2013Hadamard (HH), HH\u2013Fej\u00e9r, and Pachpatte-type inequalities for left- and right-interval-valued harmonically convex mappings (LRIVH convex mappings) with an exponential function in the kernel. We use fractional operators to develop several generalizations, capturing unique outcomes that are currently under investigation, while also introducing a new operator. Generally, we propose two methods that, in conjunction with more generalized fractional integral operators with an exponential function in the kernel, can address certain novel generalizations of increasing mappings under the assumption of LRIV convexity, yielding some noteworthy results. The results produced by applying the suggested scheme show that the computational effects are extremely accurate, flexible, efficient, and simple to implement in order to explore the path of upcoming intricate waveform and circuit theory research.<\/jats:p>","DOI":"10.3390\/axioms13090616","type":"journal-article","created":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T10:33:01Z","timestamp":1726050781000},"page":"616","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Research on New Interval-Valued Fractional Integrals with Exponential Kernel and Their Applications"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9758-5591","authenticated-orcid":false,"given":"Abdulrahman F.","family":"Aljohani","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 47512, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6076-625X","authenticated-orcid":false,"given":"Ali","family":"Althobaiti","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2678-2066","authenticated-orcid":false,"given":"Saad","family":"Althobaiti","sequence":"additional","affiliation":[{"name":"Department of Sciences and Technology, Ranyah University College, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1090\/proc\/14741","article-title":"Fractional Hermite\u2013Had amard-type inequalities for interval-valued functions","volume":"148","author":"Budak","year":"2020","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"140202","DOI":"10.1007\/s11432-023-3982-y","article-title":"Online Pareto optimal control of mean-field stochastic multi-player systems using policy iteration","volume":"67","author":"Jiang","year":"2024","journal-title":"Sci. China Inf. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"155417","DOI":"10.1103\/PhysRevB.109.155417","article-title":"Valley quantum interference modulated by hyperbolic shear polaritons","volume":"109","author":"Jia","year":"2023","journal-title":"Phys. Rev. B"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1007\/s00010-019-00642-z","article-title":"An extension of the Hermite\u2013Hadamard inequality for convex and s-convex functions","volume":"93","year":"2019","journal-title":"Aequ. Math."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1134\/S0001434617110013","article-title":"Fej\u00e9r and Hermite\u2013Hadamard type inequalities for N-quasi-convex functions","volume":"102","author":"Abramovich","year":"2017","journal-title":"Math. Notes"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"329","DOI":"10.7153\/jmi-2020-14-22","article-title":"A mapping associated to h-convex version of the Hermite\u2013Hadamard inequality with applications","volume":"14","author":"Delavar","year":"2020","journal-title":"J. Math. Inequal."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1033","DOI":"10.1007\/s13398-017-0408-5","article-title":"Hermite Hadamard type inequalities for conformable fractional integrals","volume":"112","author":"Khan","year":"2018","journal-title":"Rev. R. Acad. Cienc. Exactas F\u00eds. Nat. Ser. A Math. RACSAM"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"850","DOI":"10.1080\/00029890.2020.1803648","article-title":"A very short proof of the Hermite Hadamard inequalities","volume":"127","author":"Marinescu","year":"2020","journal-title":"Am. Math. Month."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1002\/num.22521","article-title":"Weighted Hermite\u2013Hadamard\u2013Mercer type inequali ties for convex functions","volume":"37","year":"2021","journal-title":"Numer. Methods Part. Differ. Equ."},{"key":"ref_10","first-page":"77","article-title":"Hermite-Hadamard type inequalities for multiplicatively geometrically P-functions Poincare","volume":"2","author":"Kadakal","year":"2018","journal-title":"J. Anal. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"105","DOI":"10.46753\/pjaa.2019.v06i02.004","article-title":"New inequalities for AH-convex functions using beta and hypergeometric functions","volume":"2","author":"Kadakal","year":"2019","journal-title":"Poincare J. Anal. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.cam.2018.12.030","article-title":"Hermite Hadamard, Hermite\u2013Hadamard\u2013Fej\u00e9r, Dragomir\u2013Agarwal and Pachpatte type inequalities for convex functions via new fractional integrals","volume":"353","author":"Ahmad","year":"2019","journal-title":"J. Comput. Appl. Math."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"642","DOI":"10.1080\/00036811.2019.1616083","article-title":"Some k-fractional extensions of the trapezium inequalities through generalized relative semi-(m,h)-preinvexity","volume":"100","author":"Du","year":"2021","journal-title":"Appl. Anal."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2314","DOI":"10.1002\/mma.5784","article-title":"Hermite\u2013Hadamard inequalities for Riemann Liouville fractional integrals of a convex function with respect to a monotone function","volume":"44","author":"Mohammed","year":"2021","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1274","DOI":"10.1016\/j.jmaa.2016.09.018","article-title":"Hermite\u2013Hadamard and Hermite Hadamard\u2013Fej\u00e9r type inequalities for generalized fractional integrals","volume":"446","author":"Chen","year":"2017","journal-title":"J. Math. Anal. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/j.cam.2018.10.022","article-title":"New Hermite-Hadamard type integral inequalities for convex functions and their applications","volume":"350","author":"Mehrez","year":"2019","journal-title":"J. Comput. Appl. Math."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.18514\/MMN.2018.2441","article-title":"Improvement of fractional Hermite\u2013Hadamard type inequality for convex functions","volume":"19","author":"Kunt","year":"2018","journal-title":"Miskolc Math. Notes"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1145\/142920.134024","article-title":"Interval analysis for computer graphics","volume":"26","author":"Snyder","year":"1992","journal-title":"ACM SIGGRAPH Comput. Graph."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"638","DOI":"10.1109\/TNN.2008.2011267","article-title":"Neural network output optimization using interval analysis","volume":"20","author":"Chu","year":"2009","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1109\/TE.2011.2109722","article-title":"Automatic error analysis using intervals","volume":"55","author":"Rothwell","year":"2012","journal-title":"IEEE Trans. Educ."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4835","DOI":"10.1007\/s00603-024-03788-8","article-title":"Quantifying Post-peak Behavior of Rocks with Type-I, Type-II, and Mixed Fractures by Developing a Quasi-State-Based Peridynamics","volume":"57","author":"Tian","year":"2024","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2316107","DOI":"10.1080\/17538947.2024.2316107","article-title":"Mitigation of tropospheric delay induced errors in TS-InSAR ground deformation monitoring","volume":"17","author":"Guo","year":"2024","journal-title":"Int. J. Digit. Earth"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/s40096-021-00445-x","article-title":"On the fractional integral inclusions having exponential kernels for interval-valued convex functions","volume":"17","author":"Zhou","year":"2023","journal-title":"Math. Sci."},{"key":"ref_24","first-page":"1","article-title":"Certain fractional integral inclusions pertaining to interval-valued exponential trigonometric convex functions","volume":"17","author":"Zhou","year":"2023","journal-title":"J. Math. Inequal."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"113274","DOI":"10.1016\/j.chaos.2023.113274","article-title":"On fuzzy fractional integral operators having exponential kernels and related certain inequalities for exponential trigonometric convex fuzzy-number valued mappings","volume":"169","author":"Khan","year":"2023","journal-title":"Chaos Solitons Fractals"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Khan, M.B., C\u0103ta\u015f, A., Aloraini, N., and Soliman, M.S. (2023). Some new versions of fractional inequalities for exponential trigonometric convex mappings via ordered relation on interval-valued settings. Fractal Fract., 7.","DOI":"10.3390\/fractalfract7030223"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Khan, M.B., Mac\u00edas-D\u00edaz, J.E., Althobaiti, A., and Althobaiti, S. (2023). Some new properties of exponential trigonometric convex functions using up and down relations over fuzzy numbers and related inequalities through fuzzy fractional integral operators having exponential kernels. Fractal Fract., 7.","DOI":"10.3390\/fractalfract7070567"},{"key":"ref_28","unstructured":"Dimitrijev, S. (1997). Effective Mass in Semiconductors, Bart. J. Van Zeghbroeck\/University of Colorado."},{"key":"ref_29","first-page":"237","article-title":"Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals","volume":"238","author":"Iscan","year":"2014","journal-title":"Appl. Math. Comput."},{"key":"ref_30","first-page":"1","article-title":"Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integrals","volume":"18","author":"Iscan","year":"2015","journal-title":"RGMIA Res. Rep. Collect."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Khan, M.B., Mac\u00edas-D\u00edaz, J.E., Trean\u021b\u01ce, S., Soliman, M.S., and Zaini, H.G. (2022). Hermite-Hadamard Inequalities in Fractional Calculus for Left and Right Harmonically Convex Functions via Interval-Valued Settings. Fractal Fract., 6.","DOI":"10.3390\/fractalfract6040178"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.fss.2020.06.003","article-title":"Jensen\u2019s inequalities for set-valued and fuzzy set-valued functions","volume":"404","author":"Zhang","year":"2020","journal-title":"Fuzzy Sets Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"129969","DOI":"10.1016\/j.jhydrol.2023.129969","article-title":"Study on optimization and combination strategy of multiple daily runoff prediction models coupled with physical mechanism and LSTM","volume":"624","author":"Guo","year":"2023","journal-title":"J. Hydrol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"3953","DOI":"10.1007\/s11269-024-03848-2","article-title":"Single-Objective and Multi-Objective Flood Interval Forecasting Considering Interval Fitting Coefficients","volume":"38","author":"Chang","year":"2024","journal-title":"Water Resour. Manag."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1186\/s40001-024-01681-2","article-title":"Automated localization of mandibular landmarks in the construction of mandibular median sagittal plane","volume":"29","author":"Wang","year":"2024","journal-title":"Eur. J. Med. Res."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1403","DOI":"10.2991\/ijcis.d.210409.001","article-title":"Some new classes of preinvex fuzzy-interval-valued functions and inequalities","volume":"14","author":"Khan","year":"2021","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1809","DOI":"10.2991\/ijcis.d.210620.001","article-title":"Harmonically convex fuzzy-interval-valued functions and fuzzy-interval Riemann-Liouville fractional integral inequalities","volume":"14","author":"Sana","year":"2021","journal-title":"Int. J. Comput. Intell. 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