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Öğe Deriving weighted Newton-type inequalities for diverse function classes through Riemann-Liouville fractional integrals(Pergamon-Elsevier Science Ltd, 2024) Almoneef, Areej A.; Hyder, Abd-Allah; Budak, HüseyinThis study introduces weighted Newton-type inequalities for diverse function classes via Riemann-Liouville fractional integrals. We begin by employing a positive weighted function to demonstrate a crucial integral equality which necessary for establishing the main outcomes. Leveraging this equality along with Riemann- Liouville fractional integrals, we prove several weighted Newton-type inequalities for various function classes, including differentiable convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation. From the obtained results, one can get an insights into the implications of Newton-type inequalities and outlines potential avenues for future research endeavors.Öğe Development of Fractional Newton-Type Inequalities Through Extended Integral Operators(Mdpi, 2025) Hyder, Abd-Allah; Almoneef, Areej A.; Barakat, Mohamed A.; Budak, Huseyin; Aktas, OzgeThis paper introduces a new class of Newton-type inequalities (NTIs) within the framework of extended fractional integral operators. This study begins by establishing a fundamental identity for generalized fractional Riemann-Liouville (FR-L) operators, which forms the basis for deriving various inequalities under different assumptions on the integrand. In particular, fractional counterparts of the classical 1/3 and 3/8 Simpson rules are obtained when the modulus of the first derivative is convex. The analysis is further extended to include functions that satisfy a Lipschitz condition or have bounded first derivatives. Moreover, an additional NTI is presented for functions of bounded variation, expressed in terms of their total variation. In all scenarios, the proposed results reduce to classical inequalities when the fractional parameters are specified accordingly, thus offering a unified perspective on numerical integration through fractional operators.Öğe Fractional Milne-type inequalities for twice differentiable functions(Amer Inst Mathematical Sciences-Aims, 2024) Almoneef, Areej A.; Hyder, Abd-Allah; Budak, Hüseyin; Barakat, Mohamed A.In this study, a specific identity was derived for functions that possess two continuous derivatives. Through the utilization of this identity and Riemann-Liouville fractional integrals, several fractional Milne-type inequalities were established for functions whose second derivatives inside the absolute value are convex. Additionally, an example and a graphical representation are included to clarify the core findings of our research.Öğe Further Midpoint Inequalities via Generalized Fractional Operators in Riemann-Liouville Sense(Mdpi, 2022) Hyder, Abd-Allah; Budak, Hüseyin; Almoneef, Areej A.In this study, new midpoint-type inequalities are given through recently generalized Riemann-Liouville fractional integrals. Foremost, we present an identity for a class of differentiable functions including the proposed fractional integrals. Then, several midpoint-type inequalities containing generalized Riemann-Liouville fractional integrals are proved by employing the features of convex and concave functions. Furthermore, all obtained results in this study can be compared to previously published results.Öğe Generalized Fractional Integral Inequalities Derived from Convexity Properties of Twice-Differentiable Functions(Mdpi, 2025) Almoneef, Areej A.; Hyder, Abd-Allah; Hezenci, Fatih; Budak, HuseyinThis study presents novel formulations of fractional integral inequalities, formulated using generalized fractional integral operators and the exploration of convexity properties. A key identity is established for twice-differentiable functions with the absolute value of their second derivative being convex. Using this identity, several generalized fractional Hermite-Hadamard-type inequalities are developed. These inequalities extend the classical midpoint and trapezoidal-type inequalities, while offering new perspectives through convexity properties. Also, some special cases align with known results, and an illustrative example, accompanied by a graphical representation, is provided to demonstrate the practical relevance of the results. Moreover, the findings may offer potential applications in numerical integration, optimization, and fractional differential equations, illustrating their relevance to various areas of mathematical analysis.Öğe Improvement in Some Inequalities via Jensen-Mercer Inequality and Fractional Extended Riemann-Liouville Integrals(Mdpi, 2023) Hyder, Abd-Allah; Almoneef, Areej A.; Budak, HüseyinThe primary intent of this study is to establish some important inequalities of the Hermite-Hadamard, trapezoid, and midpoint types under fractional extended Riemann-Liouville integrals (FERLIs). The proofs are constructed using the renowned Jensen-Mercer, power-mean, and Holder inequalities. Various equalities for the FERLIs and convex functions are construed to be the mainstay for finding new results. Some connections between our main findings and previous research on Riemann-Liouville fractional integrals and FERLIs are also discussed. Moreover, a number of examples are featured, with graphical representations to illustrate and validate the accuracy of the new findings.Öğe Novel Ostrowski-Type Inequalities for Generalized Fractional Integrals and Diverse Function Classes(Mdpi, 2024) Almoneef, Areej A.; Hyder, Abd-Allah; Barakat, Mohamed A.; Budak, HuseyinIn this work, novel Ostrowski-type inequalities for dissimilar function classes and generalized fractional integrals (FITs) are presented. We provide a useful identity for differentiable functions under FITs, which results in special expressions for functions whose derivatives have convex absolute values. A new condition for bounded variation functions is examined, as well as expansions to bounded and Lipschitzian derivatives. Our comprehension is improved by comparison with current findings, and recommendations for future study areas are given.Öğe On Improved Simpson-Type Inequalities via Convexity and Generalized Fractional Operators(Wiley, 2025) Almoneef, Areej A.; Hyder, Abd-Allah; Hezenci, Fatih; Budak, HuseyinIn this work, we develop novel Simpson-type inequalities for mappings with convex properties by employing operators for tempered fractional integrals. These findings expand upon and refine classical results, including those linked to Riemann-Liouville fractional integrals. Using methodologies such as H & ouml;lder's inequality, the power-mean inequality, and convex function properties, we derive precise bounds for these inequalities. The main contributions include the derivation of Simpson-type inequalities under various convexity conditions and their adaptations for specific cases, such as functions with bounded derivatives and Lipschitz continuity. Special cases, where these inequalities reduce to classical results involving standard integrals, are also explored. Explicitly, clear connections to classical integral inequalities are established for differentiable functions whose derivatives satisfy convexity, boundedness, and Lipschitz conditions. Additionally, future research directions are proposed, emphasizing the broad applicability of these results in fractional calculus and convex analysis.Öğe On New Fractional Version of Generalized Hermite-Hadamard Inequalities(Mdpi, 2022) Hyder, Abd-Allah; Almoneef, Areej A.; Budak, Hüseyin; Barakat, Mohamed A.In this study, we establish a novel version of Hermite-Hadamard inequalities through neoteric generalized Riemann-Liouville fractional integrals (RLFIs). For functions with the convex absolute values of derivatives, we create a variety of midpoint and trapezoid form inequalities, including the generalized RLFIs. Moreover, multiple fractional inequalities can be produced as special cases of the findings of this study.Öğe Simpson-type inequalities by means of tempered fractional integrals(Amer Inst Mathematical Sciences-Aims, 2023) Almoneef, Areej A.; Hyder, Abd-Allah; Hezenci, Fatih; Budak, HüseyinThe latest iterations of Simpson-type inequalities (STIs) are the topic of this paper. These inequalities were generated via convex functions and tempered fractional integral operators (TFIOs). To get these sorts of inequalities, we employ the well-known Ho center dot lder inequality and the inequality of exponent mean. The subsequent STIS are a generalization of several works on this topic that use the fractional integrals of Riemann-Liouville (FIsRL). Moreover, distinctive outcomes can be achieved through unique selections of the parameters.Öğe Weighted fractional Euler-Maclaurin inequalities for convex and bounded variation functions via Riemann-Liouville integrals(Springer, 2025) Almoneef, Areej A.; Hyder, Abd-Allah; Hezenci, Fatih; Budak, HueseyinThis paper develops weighted Euler-Maclaurin-type inequalities using Riemann-Liouville fractional integrals for classes of differentiable convex functions and functions of bounded variation. The work begins with a foundational integral equality that incorporates a positive weighting function, which serves as the basis for constructing these Euler-Maclaurin-type inequalities. Through this approach, we derive specific fractional inequalities for convex functions and extend them to functions of bounded variation, addressing key accuracy bounds and demonstrating flexibility across applications. Some remarks and particular cases are discussed to provide deeper observation, showcasing variations of the derived inequalities under particular function classes and conditions. This exploration offers a comprehensive view of the potential extensions of weighted fractional inequalities within the context of fractional calculus.Öğe Weighted Milne-type inequalities through Riemann-Liouville fractional integrals and diverse function classes(Amer Inst Mathematical Sciences-Aims, 2024) Almoneef, Areej A.; Hyder, Abd-Allah; Budak, HüseyinThis research paper investigated weighted Milne-type inequalities utilizing RiemannLiouville fractional integrals across diverse function classes. A key contribution lies in the establishment of a fundamental integral equality, facilitated by the use of a nonnegative weighted function, which is pivotal for deriving the main results. The paper systematically proved weighted Milne-type inequalities for various function classes, including differentiable convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation. The obtained results not only contribute to the understanding of Milne-type inequalities but also offer insights that pave the way for potential future research in the considered topics. Furthermore, it is evident that the results obtained encompass numerous findings that were previously presented in various studies as special cases.