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    Certain fractional inequalities via the Caputo Fabrizio operator
    (Univ Nis, Fac Sci Math, 2023) Qaisar, Shahid; Munir, Arslan; Budak, Huseyin
    The Caputo Fabrizio fractional integral operator is one of the key concepts in fractional calculus. It is involved in many concrete and practical issues. In the present study, we have discussed some novel ideas to fractional Hermite-Hadamard inequalities within a Caputo Fabrizio fractional integral framework. The fractional integral under investigation is used to establish some new fractional Hermite-Hadamard inequalities. The findings of this study can be seen as a generalization and extension of numerous earlier inequalities via convex function. In addition, we demonstrate a few applications of our findings to special means of real numbers.
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    Error Bounds for Fractional Integral Inequalities with Applications
    (Mdpi, 2024) Alqahtani, Nouf Abdulrahman; Qaisar, Shahid; Munir, Arslan; Naeem, Muhammad; Budak, Huseyin
    Fractional calculus has been a concept used to obtain new variants of some well-known integral inequalities. In this study, our main goal is to establish the new fractional Hermite-Hadamard, and Simpson's type estimates by employing a differentiable function. Furthermore, a novel class of fractional integral related to prominent fractional operator (Caputo-Fabrizio) for differentiable convex functions of first order is proven. Then, taking this equality into account as an auxiliary result, some new estimation of the Hermite-Hadamard and Simpson's type inequalities as generalization is presented. Moreover, few inequalities for concave function are obtained as well. It is observed that newly established outcomes are the extension of comparable inequalities existing in the literature. Additionally, we discuss the applications to special means, matrix inequalities, and the q-digamma function.
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    Generalizations of Simpson type inequality for (?, m)-convex functions
    (Univ Nis, Fac Sci Math, 2024) Munir, Arslan; Budak, Huseyin; Faiz, Irza; Qaisar, Shahid
    Several scholars are interested in fractional operators with integral inequalities. Due to its characteristics and wide range of applications in science, engineering fields, artificial intelligence and fractional inequalities should be employed in mathematical investigations. In this paper, we establish the new identity for the Caputo-Fabrizio fractional integral operator. By utilizing this identity, the generalization of Simpson type inequality for ( alpha, m ) -convex functions via the Caputo-Fabrizio fractional integral operator. Furthermore, we also include the applications to special means, q -digamma functions, Simpson formula, Matrix inequalities, Modified Bessel function, and mind -point formula. These applications have given a new dimension to scholars.
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    Some new fractional corrected Euler-Maclaurin type inequalities for function whose second derivatives are s-convex function
    (Taylor & Francis Inc, 2024) Munir, Arslan; Vivas-Cortez, Miguel; Qayyum, Ather; Budak, Huseyin; Faiz, Irza; Supadi, Siti Suzlin
    Fractional integrals and inequalities have gained a lot of attention in recent years. By introducing innovative analytical approaches and applications, and by applying these approaches, numerous forms of inequalities have been examined. In this paper, we establish new identity for the twice differentiable function where the absolute value is convex. By utilizing this identity, numerous Corrected Euler-Maclaurin-type inequalities are developed for the Caputo-Fabrizio fractional integral operator. Based on this identity, the Corrected Euler-Maclaurin-type inequalities for $s$s-convex function are obtained. By employing well-known inequalities such as H & ouml;lder's and Power -Mean, we are introduced several new error bounds and estimates for Corrected Euler-Maclaurin-type inequalities. Additionally, special cases of the present results are applied to obtain the previous well-known results.
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    A Study of Some New Hermite-Hadamard Inequalities via Specific Convex Functions with Applications
    (Mdpi, 2024) Junjua, Moin-ud-Din; Qayyum, Ather; Munir, Arslan; Budak, Huseyin; Saleem, Muhammad Mohsen; Supadi, Siti Suzlin
    Convexity plays a crucial role in the development of fractional integral inequalities. Many fractional integral inequalities are derived based on convexity properties and techniques. These inequalities have several applications in different fields such as optimization, mathematical modeling and signal processing. The main goal of this article is to establish a novel and generalized identity for the Caputo-Fabrizio fractional operator. With the help of this specific developed identity, we derive new fractional integral inequalities via exponential convex functions. Furthermore, we give an application to some special means.