Yazar "O'Regan, Donal" seçeneğine göre listele

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    An application of decision theory on the approximation of a generalized Apollonius-type quadratic functional equation
    (Springer, 2024) Ahadi, Azam; Saadati, Reza; Allahviranloo, Tofigh; O'Regan, Donal
    To make better decisions on approximation, we may need to increase reliable and useful information on different aspects of approximation. To enhance information about the quality and certainty of approximating the solution of an Apollonius-type quadratic functional equation, we need to measure both the quality and the certainty of the approximation and the maximum errors. To measure the quality of it, we use fuzzy sets, and to achieve its certainty, we use the probability distribution function. To formulate the above problem, we apply the concept of Z-numbers and introduce a special matrix of the form diag(A,B,C)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{diag}(A, B, C)$\end{document} (named the generalized Z-number) where A is a fuzzy time-stamped set, B is the probability distribution function, and C is a degree of reliability of A that is described as a value of A*B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A\ast B$\end{document}. Using generalized Z-numbers, we define a novel control function to investigate H-U-R stability to approximate the solution of an Apollonius-type quadratic functional equation with quality and certainty of the approximation.
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    Fuzzy control problem via random multi-valued equations in symmetric F-n-NLS
    (MDPI, 2022) Saadati, Reza; Allahviranloo, Tofigh; O'Regan, Donal; Alshammari, Fehaid Salem
    To study an uncertain case of a control problem, we consider the symmetric F-n-NLS which is induced by a dynamic norm inspired by a random norm, distribution functions, and fuzzy sets. In this space, we consider a random multi-valued equation containing a parameter and investigate existence, and unbounded continuity of the solution set of it. As an application of our results, we consider a control problem with multi-point boundary conditions and a second order derivative operator.
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    Solving the Fornberg-Whitham Model Derived from Gilson-Pickering Equations by Analytical Methods
    (Mdpi, 2024) O'Regan, Donal; Aderyani, Safoura Rezaei; Saadati, Reza; Allahviranloo, Tofigh
    This paper focuses on obtaining traveling wave solutions of the Fornberg-Whitham model derived from Gilson-Pickering equations, which describe the prorogation of waves in crystal lattice theory and plasma physics by some analytical techniques, i.e., the exp-function method (EFM), the multi-exp function method (MEFM) and the multi hyperbolic tangent method (MHTM). We analyze and compare them to show that MEFM is the optimum method.