Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article On Multiplicative Fractional Operators of Hadamard and Katugampola Types in G-Calculus and Related Hermite-Hadamard Inequalities(World Scientific Publ Co Pte Ltd, 2026) Abdeljawad, Thabet; Lakhdari, Abdelghani; Jarad, Fahd; Budak, Hüseyin; Alqudah, Manar AThis paper explores the extension of classical fractional operators to the framework of G-calculus, a non-Newtonian calculus in which differentiation and integration are defined via multiplicative analogs of their classical counterparts. We begin by recalling key concepts from both fractional calculus and G-calculus. Next, we revisit the recently introduced multiplicative Riemann-Liouville fractional operators and extend the multiplicative Riemann-Liouville fractional derivative to arbitrary order alpha > 0. Building on this foundation, we introduce multiplicative versions of the Hadamard and Katugampola fractional integrals and derivatives. Finally, we establish Hermite-Hadamard inequalities for both newly defined integrals.Article On the Generalized Hermite-Hadamard Inequalities via the Tempered Fractional Integrals(MDPI AG, 2020) Baleanu, Dumitru; Mohammed, Pshtiwan Othman; Sarikaya, Mehmet ZekiArticle Citation - WoS: 23Citation - Scopus: 23Ostrowski Type Inequalities Via New Fractional Conformable Integrals(Amer inst Mathematical Sciences-aims, 2019) Set, Erhan; Akdemir, Ahmet Ocak; Gozpinar, Abdurrahman; Jarad, Fahd; Rashid, Saima; Safdar, Farhat; Noor, Muhammad Aslam; Noor, Khalida InayatIn this present study, firstly, some necessary definitions and some results related to Riemann-Liouville fractional and new fractional conformable integral operators defined by Jarad et al. [13] are given. As a second, a new identity has been proved. By using this identity, new Ostrowski type inequalities has obtained involving fractional conformable integral operators. Also, some new inequalities has established for AG-convex functions via fractional conformable integrals in this study. Relevant connections of the results presented here with those earlier ones are also pointed out.Article Citation - WoS: 16Citation - Scopus: 14On Multiparametrized Integral Inequalities Via Generalized Α-Convexity on Fractal Set(Wiley, 2025) Xu, Hongyan; Lakhdari, Abdelghani; Jarad, Fahd; Abdeljawad, Thabet; Meftah, BadreddineThis article explores integral inequalities within the framework of local fractional calculus, focusing on the class of generalized alpha-convex functions. It introduces a novel extension of the Hermite-Hadamard inequality and derives numerous fractal inequalities through a novel multiparameterized identity. The primary aim is to generalize existing inequalities, highlighting that previously established results can be obtained by setting specific parameters within the main inequalities. The validity of the derived results is demonstrated through an illustrative example, accompanied by 2D and 3D graphical representations. Lastly, the paper discusses potential practical applications of these findings.Article Citation - WoS: 11Citation - Scopus: 12Hermite-Hadamard Type Inclusions Via Generalized Atangana-Baleanu Fractional Operator With Application(Amer inst Mathematical Sciences-aims, 2022) Jarad, Fahd; Kodamasingh, Bibhakar; Kashuri, Artion; Sahoo, Soubhagya KumarDefining new fractional operators and employing them to establish well-known integral inequalities has been the recent trend in the theory of mathematical inequalities. To take a step forward, we present novel versions of Hermite-Hadamard type inequalities for a new fractional operator, which generalizes some well-known fractional integral operators. Moreover, a midpoint type fractional integral identity is derived for differentiable mappings, whose absolute value of the first-order derivatives are convex functions. Moreover, considering this identity as an auxiliary result, several improved inequalities are derived using some fundamental inequalities such as Holder-Iscan, Jensen and Young inequality. Also, if we take the parameter rho = 1 in most of the results, we derive new results for Atangana-Baleanu equivalence. One example related to matrices is also given as an application.Article Citation - WoS: 7Citation - Scopus: 7New (P, Q)-Estimates for Different Types of Integral Inequalities Via (Α, M)-Convex Mappings(de Gruyter Poland Sp Z O O, 2020) Latif, Muhammad Amer; Rashid, Saima; Baleanu, Dumitru; Chu, Yu-Ming; Kalsoom, HumairaIn the article, we present a new (p, q)-integral identity for the first-order (p, q)-differentiable functions and establish several new (p, q)-quantum error estimations for various integral inequalities via (a alpha, m)-convexity. We also compare our results with the previously known results and provide two examples to show the superiority of our obtained results.Article Citation - WoS: 26Citation - Scopus: 23Some Hermite-Jensen Like Inequalities for Convex Functions Through a Certain Generalized Fractional Integrals and Related Results(Univ Miskolc inst Math, 2020) Akdemir, Ahmet Ocak; Nasir, Jamshed; Jarad, Fahd; Butt, Saad IhsanIn this article, in light of Jensen-Mercer inequality for functions whose derivatives in the absolute values are convex, some new Hermite-Jensen-Mercer inequalities have been obtained with the help of generalized types of fractional integral operators generated recently by specified local derivatives.Article Citation - WoS: 8Citation - Scopus: 12On New General Versions of Hermite-Hadamard Type Integral Inequalities Via Fractional Integral Operators With Mittag-Leffler Kernel(Springer, 2021) Akdemir, Ahmet Ocak; Avci Ardic, Merve; Baleanu, Dumitru; Kavurmaci onalan, HavvaThe main motivation of this study is to bring together the field of inequalities with fractional integral operators, which are the focus of attention among fractional integral operators with their features and frequency of use. For this purpose, after introducing some basic concepts, a new variant of Hermite-Hadamard (HH-) inequality is obtained for s-convex functions in the second sense. Then, an integral equation, which is important for the main findings, is proved. With the help of this integral equation that includes fractional integral operators with Mittag-Leffler kernel, many HH-type integral inequalities are derived for the functions whose absolute values of the second derivatives are s-convex and s-concave. Some classical inequalities and hypothesis conditions, such as Holder's inequality and Young's inequality, are taken into account in the proof of the findings.Article Citation - WoS: 24Citation - Scopus: 28New Discrete Inequalities of Hermite-Hadamard Type for Convex Functions(Springer, 2021) Alqudah, Manar A.; Jarad, Fahd; Mohammed, Pshtiwan Othman; Abdeljawad, ThabetWe introduce new time scales on Z. Based on this, we investigate the discrete inequality of Hermite-Hadamard type for discrete convex functions. Finally, we improve our result to investigate the discrete fractional inequality of Hermite-Hadamard type for the discrete convex functions involving the left nabla and right delta fractional sums.Article Citation - WoS: 21Citation - Scopus: 28General Raina Fractional Integral Inequalities on Coordinates of Convex Functions(Springer, 2021) Kashuri, Artion; Mohammed, Pshtiwan Othman; Meftah, Badreddine; Baleanu, DumitruIntegral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In this study, authors have established some generalized Raina fractional integral inequalities using an (l1,h1)-(l2,h2)-convex function on coordinates. Also, we obtain an integral identity for partial differentiable functions. As an effect of this result, two interesting integral inequalities for the (l1,h1)-(l2,h2)-convex function on coordinates are given. Finally, we can say that our findings recapture some recent results as special cases.