Yazar "Bin-Mohsin, Bandar" seçeneğine göre listele

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    Generalized AB-Fractional Operator Inclusions of Hermite-Hadamard's Type via Fractional Integration
    (Mdpi, 2023) Bin-Mohsin, Bandar; Awan, Muhammad Uzair; Javed, Muhammad Zakria; Khan, Awais Gul; Budak, Hüseyin; Mihai, Marcela V.; Noor, Muhammad Aslam
    The aim of this research is to explore fractional integral inequalities that involve interval-valued preinvex functions. Initially, a new set of fractional operators is introduced that uses the extended generalized Mittag-Leffler function E-mu,alpha,l(gamma,delta, k,c) (tau; p) as a kernel in the interval domain. Additionally, a new form of Atangana-Baleanu operator is defined using the same kernel, which unifies multiple existing integral operators. By varying the parameters in E-mu,alpha,l(gamma,delta, k,c)(tau; p), several new fractional operators are obtained. This study then utilizes the generalized AB integral operators and the preinvex interval-valued property of functions to establish new Hermite-Hadamard, Pachapatte, and Hermite-Hadamard-Fejer inequalities. The results are supported by numerical examples, graphical illustrations, and special cases.
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    Numerical Approximations and Fractional Calculus: Extending Boole's Rule with Riemann-LiouvilleFractional Integral Inequalities
    (Mdpi, 2025) Mateen, Abdul; Haider, Wali; Shehzadi, Asia; Budak, Huseyin; Bin-Mohsin, Bandar
    This paper develops integral inequalities for first-order differentiable convex functions within the framework of fractional calculus, extending Boole-type inequalities to this domain. An integral equality involving Riemann-Liouville fractional integrals is established, forming the foundation for deriving novel fractional Boole-type inequalities tailored to differentiable convex functions. The proposed framework encompasses a wide range of functional classes, including Lipschitzian functions, bounded functions, convex functions, and functions of bounded variation, thereby broadening the applicability of these inequalities to diverse mathematical settings. The research emphasizes the importance of the Riemann-Liouville fractional operator in solving problems related to non-integer-order differentiation, highlighting its pivotal role in enhancing classical inequalities. These newly established inequalities offer sharper error bounds for various numerical quadrature formulas in classical calculus, marking a significant advancement in computational mathematics. Numerical examples, computational analysis, applications to quadrature formulas and graphical illustrations substantiate the efficacy of the proposed inequalities in improving the accuracy of integral approximations, particularly within the context of fractional calculus. Future directions for this research include extending the framework to incorporate q-calculus, symmetrized q-calculus, alternative fractional operators, multiplicative calculus, and multidimensional spaces. These extensions would enable a comprehensive exploration of Boole's formula and its associated error bounds, providing deeper insights into its performance across a broader range of mathematical and computational settings.
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    Some Classical Inequalities Associated with Generic Identity and Applications
    (Mdpi, 2024) Javed, Muhammad Zakria; Awan, Muhammad Uzair; Bin-Mohsin, Bandar; Budak, Huseyin; Dragomir, Silvestru Sever
    In this paper, we derive a new generic equality for the first-order differentiable functions. Through the utilization of the general identity and convex functions, we produce a family of upper bounds for numerous integral inequalities like Ostrowski's inequality, trapezoidal inequality, midpoint inequality, Simpson's inequality, Newton-type inequalities, and several two-point open trapezoidal inequalities. Also, we provide the numerical and visual explanation of our principal findings. Later, we provide some novel applications to the theory of means, special functions, error bounds of composite quadrature schemes, and parametric iterative schemes to find the roots of linear functions. Also, we attain several already known and new bounds for different values of gamma and parameter xi.
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    Unified inequalities of the q-Trapezium-Jensen-Mercer type that incorporate majorization theory with applications
    (Amer Inst Mathematical Sciences-Aims, 2023) Bin-Mohsin, Bandar; Javed, Muhammad Zakria; Awan, Muhammad Uzair; Budak, Hüseyin; Khan, Awais Gul; Cesarano, Clemente; Noor, Muhammad Aslam
    The objective of this paper is to explore novel unified continuous and discrete versions of the Trapezium-Jensen-Mercer (TJM) inequality, incorporating the concept of convex mapping within the framework of q-calculus, and utilizing majorized tuples as a tool. To accomplish this goal, we establish two fundamental lemmas that utilize the & sigma;1q and & sigma;2 q differentiability of mappings, which are critical in obtaining new left and right side estimations of the midpoint q-TJM inequality in conjunction with convex mappings. Our findings are significant in a way that they unify and improve upon existing results. We provide evidence of the validity and comprehensibility of our outcomes by presenting various applications to means, numerical examples, and graphical illustrations.