Yazar "Hyder, Abd-Allah" seçeneğine göre listele

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    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, Hüseyin
    This 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.
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    Development of Fractional Newton-Type Inequalities Through Extended Integral Operators
    (Mdpi, 2025) Hyder, Abd-Allah; Almoneef, Areej A.; Barakat, Mohamed A.; Budak, Huseyin; Aktas, Ozge
    This 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.
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    Enhanced bounds for Riemann-Liouville fractional integrals: Novel variations of Milne inequalities
    (Amer Inst Mathematical Sciences-Aims, 2023) Budak, Hüseyin; Hyder, Abd-Allah
    In this research article, we present novel extensions of Milne type inequalities to the realm of Riemann-Liouville fractional integrals. Our approach involves exploring significant functional classes, including convex functions, bounded functions, Lipschitzian functions and functions of bounded variation. To accomplish our objective, we begin by establishing a crucial identity for differentiable functions. Leveraging this identity, we subsequently derive new variations of fractional Milne inequalities.
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    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.
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    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.
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    Generalized Fractional Integral Inequalities Derived from Convexity Properties of Twice-Differentiable Functions
    (Mdpi, 2025) Almoneef, Areej A.; Hyder, Abd-Allah; Hezenci, Fatih; Budak, Huseyin
    This 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.
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    Improvement in Some Inequalities via Jensen-Mercer Inequality and Fractional Extended Riemann-Liouville Integrals
    (Mdpi, 2023) Hyder, Abd-Allah; Almoneef, Areej A.; Budak, Hüseyin
    The 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.
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    Milne-Type inequalities via expanded fractional operators: A comparative study with different types of functions
    (Amer Inst Mathematical Sciences-Aims, 2024) Hyder, Abd-Allah; Budak, Hüseyin; Barakat, Mohamed A.
    This study focused on deriving Milne-type inequalities using expanded fractional integral operators. We began by establishing a key equality associated with these operators. Using this equality, we explored Milne-type inequalities for functions with convex derivatives, supported by an illustrative example for clarity. Additionally, we investigated Milne-type inequalities for bounded and Lipschitzian functions utilizing fractional expanded integrals. Finally, we extended our exploration to Milne-type inequalities involving functions of bounded variation.
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    New Versions of Midpoint Inequalities Based on Extended Riemann-Liouville Fractional Integrals
    (Mdpi, 2023) Hyder, Abd-Allah; Budak, Hueseyin; Barakat, Mohamed A.
    This study aims to prove some midpoint-type inequalities for fractional extended Riemann-Liouville integrals. Crucial equality is proven to build new results. Using this equality, several midpoint-type inequalities are established via differentiable convex functions and the proposed extended fractional operators. To be more specific, the well-known Holder, Jensen, and power mean integral inequalities are employed in the demonstrated inequalities. Additionally, many remarks based on specific selections of the main results are presented. Moreover, to illustrate the key conclusions, a few instances are provided.
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    Novel Ostrowski-Type Inequalities for Generalized Fractional Integrals and Diverse Function Classes
    (Mdpi, 2024) Almoneef, Areej A.; Hyder, Abd-Allah; Barakat, Mohamed A.; Budak, Huseyin
    In 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.
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    On Improved Simpson-Type Inequalities via Convexity and Generalized Fractional Operators
    (Wiley, 2025) Almoneef, Areej A.; Hyder, Abd-Allah; Hezenci, Fatih; Budak, Huseyin
    In 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.
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    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.
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    Simpson-type inequalities by means of tempered fractional integrals
    (Amer Inst Mathematical Sciences-Aims, 2023) Almoneef, Areej A.; Hyder, Abd-Allah; Hezenci, Fatih; Budak, Hüseyin
    The 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.
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    Some New Improvements for Fractional Hermite-Hadamard Inequalities by Jensen-Mercer Inequalities
    (Wiley, 2024) Alshehri, Maryam Gharamah Ali; Hyder, Abd-Allah; Budak, Huseyin; Barakat, Mohamed A.
    This article's objective is to introduce a new double inequality based on the Jensen-Mercer JM inequality, known as the Hermite-Hadamard-Mercer inequality. We use the JM inequality to build a number of generalized trapezoid-type inequalities. Moreover, in addition to the JM inequality, we also use the H & ouml;lder inequality and the power mean inequality. Finally, a few examples are given to highlight the main points of our outcomes.
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    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, Hueseyin
    This 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.
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    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, Hüseyin
    This 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.