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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 Parameterized Quantum Simpson's and Quantum Newton's Integral Inequalities via Quantum Differentiable Convex Mappings
    (Hindawi Ltd, 2021) You, Xue Xiao; Ali, Muhammad Aamir; Budak, Hüseyin; Vivas-Cortez, Miguel J. J.; Qaisar, Shahid
    In this work, two generalized quantum integral identities are proved by using some parameters. By utilizing these equalities, we present several parameterized quantum inequalities for convex mappings. These quantum inequalities generalize many of the important inequalities that exist in the literature, such as quantum trapezoid inequalities, quantum Simpson's inequalities, and quantum Newton's inequalities. We also give some new midpoint-type inequalities as special cases. The results in this work naturally generalize the results for the Riemann integral.