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Öğe Bounds for the Error in Approximating a Fractional Integral by Simpson's Rule(Mdpi, 2023) Budak, Hueseyin; Hezenci, Fatih; Kara, Hasan; Sarikaya, Mehmet ZekiDaha fazla Simpson's rule is a numerical method used for approximating the definite integral of a function. In this paper, by utilizing mappings whose second derivatives are bounded, we acquire the upper and lower bounds for the Simpson-type inequalities by means of Riemann-Liouville fractional integral operators. We also study special cases of our main results. Furthermore, we give some examples with graphs to illustrate the main results. This study on fractional Simpson's inequalities is the first paper in the literature as a method.Daha fazla Öğe Bullen-type inequalities for twice-differentiable functions by using conformable fractional integrals(Springer, 2024) Hezenci, Fatih; Budak, HueseyinDaha fazla In this paper, we prove an equality for twice-differentiable convex functions involving the conformable fractional integrals. Moreover, several Bullen-type inequalities are established for twice-differentiable functions. More precisely, conformable fractional integrals are used to derive such inequalities. Furthermore, sundry significant inequalities are obtained by taking advantage of the convexity, Holder inequality, and power-mean inequality. Finally, we provide our results by using special cases of obtained theorems.Daha fazla Öğe Certain Simpson-type inequalities for twice-differentiable functions by conformable fractional integrals(Kangwon-Kyungki Mathematical Soc, 2023) Hezenci, Fatih; Budak, HuseyinDaha fazla In this paper, an equality is established by twice-differentiable convex functions with respect to the conformable fractional integrals. Moreover, several Simpson-type inequalities are presented for the case of twice-differentiable convex functions via conformable fractional integrals by using the established equality. Fur-thermore, our results are provided by using special cases of obtained theorems.Daha fazla Öğe A comprehensive study on Milne-type inequalities with tempered fractional integrals(Springer, 2024) Haider, Wali; Budak, Huseyin; Shehzadi, Asia; Hezenci, Fatih; Chen, HaiboDaha fazla In the framework of tempered fractional integrals, we obtain a fundamental identity for differentiable convex functions. By employing this identity, we derive several modifications of fractional Milne inequalities, providing novel extensions to the domain of tempered fractional integrals. The research comprehensively examines significant functional classes, including convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation.Daha fazla Öğe Conformable fractional Newton-type inequalities with respect to differentiable convex functions(Springer, 2023) uenal, Cihan; Hezenci, Fatih; Budak, HueseyinDaha fazla The authors propose a new method of investigation of an integral identity according to conformable fractional operators. Moreover, some Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly established equality. In addition, we prove several Newton-type inequalities with the aid of Holder and power-mean inequalities. Furthermore, several new results are given by using special choices of the obtained inequalities. Finally, we give several inequalities of conformable fractional Newton-type for functions of bounded variation.Daha fazla Öğe Conformable fractional versions of Hermite-Hadamard-type inequalities for twice-differentiable functions(Springer, 2023) Hezenci, Fatih; Kara, Hasan; Budak, HuseyinDaha fazla In this paper, new inequalities for the left and right sides of the Hermite-Hadamard inequality are acquired for twice-differentiable mappings. Conformable fractional integrals are used to derive these inequalities. Furthermore, we provide our results by using special cases of obtained theorems.Daha fazla Öğe An extensive study on parameterized inequalities for conformable fractional integrals(Springer Basel Ag, 2023) Hezenci, Fatih; Budak, HuseyinDaha fazla This paper proves an equality for the case of differentiable convex functions including the conformable fractional integrals. By using this equality, we establish several parameterized inequalities with the help of the conformable fractional integrals. Several inequalities are obtained by taking advantage of the convexity, the Holder inequality, and the power mean inequality. Furthermore, we present previously achieved results and new results by using special cases of the obtained theorems.Daha fazla Öğe Fractional Euler-Maclaurin-type inequalities for various function classes(Springer Heidelberg, 2024) Hezenci, Fatih; Budak, HuseyinDaha fazla This paper investigates a technique that uses Riemann-Liouville fractional integrals to study several Euler-Maclaurin-type inequalities for various function classes. Afterwards, we provide our results by using special cases of obtained theorems and This paper is to derive examples. Moreover, we give some Euler-Maclaurin-type inequalities for bounded functions by fractional integrals. Furthermore, we construct some fractional Euler-Maclaurin-type inequalities for Lipschitzian functions. Finally, we offer some Euler-Maclaurin-type inequalities by fractional integrals of bounded variation.Daha fazla Öğe Fractional inequalities of corrected Euler-Maclaurin-type for twice-differentiable functions(Springer Heidelberg, 2023) Hezenci, FatihDaha fazla In this article, an identity is proved for the case of twice-differentiable functions whose second derivatives in absolute value are convex. With the help of this equality, several corrected Euler-Maclaurin-type inequalities are established using the Riemann-Liouville fractional integrals. Several important fractional inequalities are obtained by taking advantage of the convexity, the Holder inequality, and the power mean inequality. Furthermore, the results are presented using special cases of obtained theories.Daha fazla Öğe Fractional midpoint-type inequalities for twice-differentiable functions(Univ Nis, Fac Sci Math, 2023) Hezenci, Fatih; Bohner, Martin; Budaka, HuseyinDaha fazla In this research article, we obtain an identity for twice differentiable functions whose second derivatives in absolute value are convex. By using this identity, we prove several left Hermite-Hadamard-type inequalities for the case of Riemann-Liouville fractional integrals. Furthermore, we provide our results by using special cases of obtained theorems.Daha fazla Öğe Fractional Newton-type integral inequalities by means of various function classes(Wiley, 2024) Hezenci, Fatih; Budak, HuseyinDaha fazla The authors of the paper present a method to examine some Newton-type inequalities for various function classes using Riemann-Liouville fractional integrals. Namely, some fractional Newton-type inequalities are established by using convex functions. In addition, several fractional Newton-type inequalities are proved by using bounded functions by fractional integrals. Moreover, we construct some fractional Newton-type inequalities for Lipschitzian functions. Furthermore, several Newton-type inequalities are acquired by fractional integrals of bounded variation. Finally, we provide our results by using special cases of obtained theorems and examples.Daha fazla Öğe Fractional Simpson-Type Inequalities for Twice Differentiable Functions(Univ Maragheh, 2023) Budak, Hueseyin; Kara, Hasan; Hezenci, FatihDaha fazla In the literature, several papers are devoted to inequal-ities of Simpson-type in the case of differentiable convex functions and fractional versions. Moreover, some papers are focused on in-equalities of Simpson-type for twice differentiable convex functions. In this research article, we obtain an identity for twice differentiable convex functions. Then, we prove several fractional inequalities of Simpson-type for convex functions.Daha fazla Öğe Fractional trapezoid and newton type inequalities for differentiable s-convex functions(Honam Mathematical Soc, 2023) Hezenci, Fatih; Budak, Huseyin; Ali, Muhammad AamirDaha fazla In the present paper, we prove that our main inequality re-duces to some trapezoid and Newton type inequalities for differentiable s-convex functions. These inequalities are established by using the well-known Riemann-Liouville fractional integrals. With the help of special cases of our main results, we also present some new and previously obtained trapezoid and Newton type inequalities.Daha fazla Öğe Generalized fractional midpoint type inequalities for co-ordinated convex functions(University of Nis, 2023) Hezenci, Fatih; Budak, Hüseyin; Kara, Hasan; Sarıkaya, Mehmet ZekiDaha fazla In this research paper, we investigate generalized fractional integrals to obtain midpoint type inequalities for the co-ordinated convex functions. First of all, we establish an identity for twice partially differentiable mappings. By utilizing this equality, some midpoint type inequalities via generalized fractional integrals are proved. We also show that the main results reduce some midpoint inequalities given in earlier works for Riemann integrals and Riemann-Liouville fractional integrals. Finally, some new inequalities for k-Riemann-Liouville fractional integrals are presented as special cases of our results. © 2023, University of Nis. All rights reserved.Daha fazla Öğe Generalized Hermite-Hadamard inclusions for a generalized fractional integral(Rocky Mt Math Consortium, 2023) Budak, Hueseyin; Kara, Hasan; Hezenci, FatihDaha fazla We introduce new generalized fractional integrals for interval-valued functions. Then we prove generalized Hermite-Hadamard type inclusions for interval-valued convex functions using these newly defined generalized fractional integrals. We also show that these results generalize several results obtained in earlier works.Daha fazla Öğe Inequalities with parameters for twice-differentiable functions involving Riemann-Liouville fractional integrals(Univ Nis, Fac Sci Math, 2024) Hezenci, FatihDaha fazla In this paper, it is given an equality for twice-differentiable functions whose second derivatives in absolute value are convex. By using this equality, it is established several left and right Hermite- Hadamard type inequalities and Simpson type inequalities for the case of Riemann-Liouville fractional integral. Namely, midpoint, trapezoid and also Simpson type inequalities are obtained for Riemann- Liouville fractional integral by using special cases of main results.Daha fazla Öğe Midpoint-type inequalities via twice-differentiable functions on tempered fractional integrals(Springer, 2023) Hezenci, Fatih; Budak, HuseyinDaha fazla In this paper, we obtain an equality involving tempered fractional integrals for twice-differentiable functions. By using this equality, we establish several left Hermite-Hadamard-type inequalities for the case of tempered fractional integrals. Moreover, we derive our results by using special cases of obtained theorems.Daha fazla Öğe New error bounds for Newton's formula associated with tempered fractional integrals(Springer, 2024) Hezenci, Fatih; Budak, HuseyinDaha fazla In this paper, we first construct an integral identity associated with tempered fractional operators. By using this identity, we have found the error bounds for Simpson's second formula, namely Newton-Cotes quadrature formula for differentiable convex functions in the framework of tempered fractional integrals and classical calculus. Furthermore, it is also shown that the newly established inequalities are the extension of comparable inequalities inside the literature.Daha fazla Öğe New Extensions of the Parameterized Inequalities Based on Riemann-Liouville Fractional Integrals(Mdpi, 2022) Kara, Hasan; Budak, Hüseyin; Hezenci, FatihDaha fazla In this article, we derive the above and below bounds for parameterized-type inequalities using the Riemann-Liouville fractional integral operators and limited second derivative mappings. These established inequalities generalized the midpoint-type, trapezoid-type, Simpson-type, and Bullen-type inequalities according to the specific choices of the parameter. Thus, a generalization of many inequalities and new results were obtained. Moreover, some examples of obtained inequalities are given for better understanding by the reader. Furthermore, the theoretical results are supported by graphs in order to illustrate the accuracy of each of the inequalities obtained according to the specific choices of the parameter.Daha fazla Öğe New generalizations of some important inequalities for Sarikaya fractional integrals(Univ Miskolc Inst Math, 2023) Hezenci, Fatih; Budak, HuseyinDaha fazla In this research paper, we investigate some new identifies for Sarikaya fractional integrals which introduced by Sarikaya and Ertugral in [20]. The fractional integral operators also have been applied to Hermite-Hadamard type integral inequalities to provide their generalized properties. Furthermore, as special cases of our main results, we present several known inequalities such as Simpson, Bullen, trapezoid for convex functions.Daha fazla

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