Browsing by Author "Akdemir, Ahmet Ocak"

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Citation - WoS: 3
Citation - Scopus: 25
New Extensions of Hermite-Hadamard Inequalities Via Generalized Proportional Fractional Integral
(Wiley, 2024) Mumcu, Ilker; Set, Erhan; Akdemir, Ahmet Ocak; Jarad, Fahd; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The main aim this work is to give Hermite-Hadamard inequalities for convex functions via generalized proportional fractional integrals. We also obtained extensions of Hermite-Hadamard type inequalities for generalized proportional fractional integrals.
New extensions of Hermite–Hadamard inequalities via generalized proportional fractional integral
(2021) Mumcu, İlker; Set, Erhan; Akdemir, Ahmet Ocak; Jarad, Fahd; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The main aim this work is to give Hermite–Hadamard inequalities for convex functions via generalized proportional fractional integrals. We also obtained extensions of Hermite–Hadamard type inequalities for generalized proportional fractional integrals. © 2021 Wiley Periodicals LLC
Citation - WoS: 2
Non-Conformable Integral Inequalities of Chebyshev-Polya Type
(Element, 2021) Akdemir, Ahmet Ocak; Agarwal, Praveen; Baleanu, Dumitru; Butt, Saad Ihsan; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Inequality studies involving new integrals and derivatives have been carried out recently. This article designed as follows, the results were obtained by using the non-conformable fractional integral operators to provide new inequalities of Polya-Szego and Chebyshev type. Some special cases have been considered for our main findings.
Citation - WoS: 8
Citation - Scopus: 12
On 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, Havva; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The 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.
Citation - WoS: 32
Citation - Scopus: 40
On Some New Weighted Inequalities for Differentiable Exponentially Convex and Exponentially Quasi-Convex Functions With Applications
(Mdpi, 2019) Rashid, Saima; Akdemir, Ahmet Ocak; Baleanu, Dumitru; Liu, Jia-Bao; Nie, Dongming; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, we aim to establish several inequalities for differentiable exponentially convex and exponentially quasi-convex mapping, which are connected with the famous Hermite-Hadamard (HH) integral inequality. Moreover, we have provided applications of our findings to error estimations in numerical analysis and higher moments of random variables.
Citation - WoS: 19
Citation - Scopus: 20
Ostrowski Type Inequalities Via New Fractional Conformable Integrals
(Amer inst Mathematical Sciences-aims, 2019) Set, Erhan; Akdemir, Ahmet Ocak; Gozpinar, Abdurrahman; Jarad, Fahd; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.
Citation - WoS: 5
Citation - Scopus: 8
Predictive Dynamical Modeling and Stability of the Equilibria in a Discrete Fractional Difference Covid-19 Epidemic Model
(Elsevier, 2023) Rashid, Saima; Akdemir, Ahmet Ocak; Khalid, Aasma; Baleanu, Dumitru; Al-Sinan, Bushra R.; Elzibar, O. A. I.; Chu, Yu-Ming; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The SARSCoV-2 virus, also known as the coronavirus-2, is the consequence of COVID-19, a severe acute respiratory syndrome. Droplets from an infectious individual are how the pathogen is transmitted from one individual to another and occasionally, these particles can contain toxic textures that could also serve as an entry point for the pathogen. We formed a discrete fractional-order COVID-19 framework for this investigation using information and inferences from Thailand. To combat the illnesses, the region has implemented mandatory vaccination, interpersonal stratification and mask distribution programs. As a result, we divided the vulnerable people into two groups: those who support the initiatives and those who do not take the influence regulations seriously. We analyze endemic problems and common data while demonstrating the threshold evolution defined by the fundamental reproductive quantity R0. Employing the mean general interval, we have evaluated the configuration value systems in our framework. Such a framework has been shown to be adaptable to changing pathogen populations over time. The Picard Lindelof technique is applied to determine the existence-uniqueness of the solution for the proposed scheme. In light of the relationship between the R0 and the consistency of the fixed points in this framework, several theoretical conclusions are made. Numerous numerical simulations are conducted to validate the outcome.
Citation - WoS: 41
Simpson's Type Integral Inequalities for Κ-Fractional Integrals and Their Applications
(Amer inst Mathematical Sciences-aims, 2019) Akdemir, Ahmet Ocak; Jarad, Fahd; Noor, Muhammad Aslam; Noor, Khalida Inayat; Rashid, Saima; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, some new inequalities of Simpson's type are set up for the classes of functions whose derivatives of absolute are preinvex by means of kappa-fractional integrals. Additionally, by extraordinary choices of n and kappa, we give some diminished outcomes. Meanwhile, we also provide the inequalities for F-divergence measures and in probabilistic versions.
Citation - WoS: 22
Citation - Scopus: 18
Some 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 Ihsan; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.