Yazar "Barakat, Mohamed A." seçeneğine göre listele

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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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    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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    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 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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    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.