Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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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: 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: 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: 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.Article Citation - WoS: 10Citation - Scopus: 12Fuzzy-Interval Inequalities for Generalized Convex Fuzzy-Interval Functions Via Fuzzy Riemann Integrals(Amer inst Mathematical Sciences-aims, 2022) Srivastava, Hari Mohan; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Jawa, Taghreed M.; Khan, Muhammad BilalThe objective of the authors is to introduce the new class of convex fuzzy-interval-valued functions (convex-FIVFs), which is known as p-convex fuzzy-interval-valued functions (p-convex-FIVFs). Some of the basic properties of the proposed fuzzy-interval-valued functions are also studied. With the help of p-convex FIVFs, we have presented some Hermite-Hadamard type inequalities (H-H type inequalities), where the integrands are FIVFs. Moreover, we have also proved the Hermite-Hadamard-Fejer type inequality (H-H Fejer type inequality) for p-convex-FIVFs. To prove the validity of main results, we have provided some useful examples. We have also established some discrete form of Jense's type inequality and Schur's type inequality for p-convex-FIVFs. The outcomes of this paper are generalizations and refinements of different results which are proved in literature. These results and different approaches may open new direction for fuzzy optimization problems, modeling, and interval-valued functions.Article Citation - WoS: 7Citation - Scopus: 7Fractional Integral Inequalities for Exponentially Nonconvex Functions and Their Applications(Mdpi, 2021) Kashuri, Artion; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Hamed, Y. S.; Srivastava, Hari MohanIn this paper, the authors define a new generic class of functions involving a certain modified Fox-Wright function. A useful identity using fractional integrals and this modified Fox-Wright function with two parameters is also found. Applying this as an auxiliary result, we establish some Hermite-Hadamard-type integral inequalities by using the above-mentioned class of functions. Some special cases are derived with relevant details. Moreover, in order to show the efficiency of our main results, an application for error estimation is obtained as well.Article Citation - WoS: 22Citation - Scopus: 24Some New Extensions for Fractional Integral Operator Having Exponential in the Kernel and Their Applications in Physical Systems(de Gruyter Poland Sp Z O O, 2020) Baleanu, Dumitru; Chu, Yu-Ming; Rashid, SaimaThe key purpose of this study is to suggest a new fractional extension of Hermite-Hadamard, Hermite-Hadamard-Fejer and Pachpatte-type inequalities for harmonically convex functions with exponential in the kernel. Taking into account the new operator, we derived some generalizations that capture novel results under investigation with the aid of the fractional operators. We presented, in general, two different techniques that can be used to solve some new generalizations of increasing functions with the assumption of convexity by employing more general fractional integral operators having exponential in the kernel have yielded intriguing results. The results achieved by the use of the suggested scheme unfold that the used computational outcomes are very accurate, flexible, effective and simple to perform to examine the future research in circuit theory and complex waveforms.Article Citation - WoS: 32Citation - Scopus: 51New Multi-Parametrized Estimates Having Pth-Order Differentiability in Fractional Calculus for Predominating H-Convex Functions in Hilbert Space(Mdpi, 2020) Kalsoom, Humaira; Hammouch, Zakia; Ashraf, Rehana; Baleanu, Dumitru; Chu, Yu-Ming; Rashid, SaimaIn Hilbert space, we develop a novel framework to study for two new classes of convex function depending on arbitrary non-negative function, which is called a predominating PLANCK CONSTANT OVER TWO PI-convex function and predominating quasiconvex function, with respect to eta, are presented. To ensure the symmetry of data segmentation and with the discussion of special cases, it is shown that these classes capture other classes of eta-convex functions, eta-quasiconvex functions, strongly PLANCK CONSTANT OVER TWO PI-convex functions of higher-order and strongly quasiconvex functions of a higher order, etc. Meanwhile, an auxiliary result is proved in the sense of kappa-fractional integral operator to generate novel variants related to the Hermite-Hadamard type for pth-order differentiability. It is hoped that this research study will open new doors for in-depth investigation in convexity theory frameworks of a varying nature.Article Citation - WoS: 93Citation - Scopus: 113On the Generalized Hermite-Hadamard Inequalities Via the Tempered Fractional Integrals(Mdpi, 2020) Sarikaya, Mehmet Zeki; Baleanu, Dumitru; Mohammed, Pshtiwan OthmanIntegral inequality plays a critical role in both theoretical and applied mathematics fields. It is clear that inequalities aim to develop different mathematical methods (numerically or analytically) and to dedicate the convergence and stability of the methods. Unfortunately, mathematical methods are useless if the method is not convergent or stable. Thus, there is a present day need for accurate inequalities in proving the existence and uniqueness of the mathematical methods. Convexity play a concrete role in the field of inequalities due to the behaviour of its definition. There is a strong relationship between convexity and symmetry. Which ever one we work on, we can apply to the other one due to the strong correlation produced between them especially in recent few years. In this article, we first introduced the notion of lambda-incomplete gamma function. Using the new notation, we established a few inequalities of the Hermite-Hadamard (HH) type involved the tempered fractional integrals for the convex functions which cover the previously published result such as Riemann integrals, Riemann-Liouville fractional integrals. Finally, three example are presented to demonstrate the application of our obtained inequalities on modified Bessel functions and q-digamma function.Article Citation - WoS: 69Citation - Scopus: 90Generation of New Fractional Inequalities Via N Polynomials S-Type Convexity With Applications(Springer, 2020) Iscan, Imdat; Baleanu, Dumitru; Chu, Yu-Ming; Rashid, SaimaThe celebrated Hermite-Hadamard and Ostrowski type inequalities have been studied extensively since they have been established. We find novel versions of the Hermite-Hadamard and Ostrowski type inequalities for the n-polynomial s-type convex functions in the frame of fractional calculus. Taking into account the new concept, we derive some generalizations that capture novel results under investigation. We present two different general techniques, for the functions whose first and second derivatives in absolute value at certain powers are n-polynomial s-type convex functions by employing K-fractional integral operators have yielded intriguing results. Applications and motivations of presented results are briefly discussed that generate novel variants related to quadrature rules that will be helpful for in-depth investigation in fractal theory, optimization and machine learning.