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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, Huseyin
    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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    Fractional Milne-type inequalities for twice differentiable functions
    (Amer Inst Mathematical Sciences-Aims, 2024) Almoneef, Areej A.; Hyder, Abd-Allah; Budak, Huseyin; 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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    Improvement in Some Inequalities via Jensen-Mercer Inequality and Fractional Extended Riemann-Liouville Integrals
    (Mdpi, 2023) Hyder, Abd-Allah; Almoneef, Areej A.; Budak, Huseyin
    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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    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, Huseyin
    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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    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, Huseyin
    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.