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Article
Computer Science, Theory & Methods
Radomir Halas et al.
Summary: The paper aims to demonstrate that the cardinality of the set of all n-ary aggregation functions defined on finite chains can be considered as a dual generalization of Dedekind numbers. The first generalization naturally arises from the commonly used definition of aggregation function. The second generalization follows in the spirit of Dedekind's original definition by showing that n-ary aggregation functions equipped with certain operations form a free algebra in a finitely generated variety over the set of n generators.
FUZZY SETS AND SYSTEMS
(2023)
Article
Computer Science, Theory & Methods
Lemnaouar Zedam et al.
Summary: In this paper, the concept of a t-norm on bounded pseudo-ordered sets and bounded trellises is introduced, along with some basic examples. The impact of abandoning transitivity is discussed, highlighting that the meet operation is not a t-norm on a proper bounded trellis, and there may be no or multiple maximal t-norms. A generic construction method is provided to extend a t-norm on an interior range of a given perpendicular to-semi-trellis to the entire trellis, with a specific instantiation based on a finite sub-trellis of right-transitive elements. The focus is also on bounded pseudo-chains and modular trellises. (c) 2023 Elsevier B.V. All rights reserved.
FUZZY SETS AND SYSTEMS
(2023)
Article
Mathematics, Applied
Chaimaa Benzarouala et al.
Summary: We prove a general fixed point theorem in the space of functions taking values in a random normed space. We then show its applications in proving Ulam stability results for the general inhomogeneous linear functional equation with several variables. We also demonstrate how to use the theorem to study approximate eigenvalues and eigenvectors of linear operators.
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Ho Vu et al.
Summary: The purpose of this paper is to discuss basic results of boundary value problems of fractional differential equations (BVP-FDEs) using the concept of Caputo fractional derivative. The existence and uniqueness of solutions for BVP-FDEs are discussed by utilizing Banach fixed point theorem and Schaefer's fixed point theorem. New sufficient conditions for ensuring the Hyers-Ulam stability and the Hyers-Ulam-Rassias stability of BVP-FDEs are also provided.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Interdisciplinary Applications
M. Sivashankar et al.
Summary: This study focuses on developing mathematical models related to the Helmholtz equation, which is considered as a second-order oscillator involving nonlinear Caputo fractional difference equations. The study also aims to determine the approximate solution of the model using the Ulam stability concept. Properties of the mathematical model in this study are also presented, and numerical simulations are provided to demonstrate the stability results.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Omar Kahouli et al.
Summary: The goal of this work is to prove the existence and uniqueness of solutions to a class of Hadamard Fractional Ito-Doob Stochastic integral equations (HFIDSIE) of order phi ∈ (0, 1) using the fixed point technique (FPT). Hyers-Ulam stability (HUS) for HFIDSIE is studied using the Gronwall inequality. Two theoretical examples are provided to illustrate the results.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Computer Science, Information Systems
Safoura Rezaei Aderyani et al.
Summary: In this paper, we apply n-ary aggregation functions to special functions to define a class of matrix-valued fuzzy controllers. These controllers help us study the Ulam-Hyers stability of (non)autonomous fractional differential systems in the Hilfer sense in matrix-valued fuzzy n-normed spaces. By using the properties of Mittag-Leffler functions, Laplace transform, and the non-standard Gronwall inequality, we propose efficient conditions for the (asymptotic) stability of the governing model in matrix fuzzy normed spaces.
INFORMATION SCIENCES
(2023)
Article
Mathematics, Applied
Safoura Rezaei Aderyani et al.
Summary: This paper investigates new approximation error estimates of a W-Hilfer fractional differential equation using well-known aggregation mappings on Mittag-Leffler-type functions, by employing a different concept of Ulam-type stability in both bounded and unbounded domains.
Article
Multidisciplinary Sciences
Naveed Khan et al.
Summary: In this paper, the dynamics of a chaotic system based on a circuit design is analyzed using the newly developed Fractal-Fractional derivative with power law kernel. The problem is modeled using classical order nonlinear, coupled ordinary differential equations, which are then generalized through Fractal-Fractional derivative with power law kernel. The theoretical analyses such as model equilibria, existence, uniqueness, and Ulam stability of the system have been calculated. A numerical technique using MATLAB software is used to analyze the highly non-linear fractal-fractional order system. The graphical solutions are presented in two dimensional graphs and three dimensional phase portraits and discussed in detail, with some concluding remarks drawn from the study. It is worth noting that fractal-fractional differential operators can quickly converge the dynamics of a chaotic system to its static equilibrium by adjusting the fractal and fractional parameters.
SCIENTIFIC REPORTS
(2023)
Article
D. Chalishajar et al.
Journal of Nonlinear Sciences and Applications
(2022)
Article
Computer Science, Theory & Methods
Safoura Rezaei Aderyani et al.
Summary: In this paper, we stabilize the tri-additive Upsilon-random operator inequality by applying the Radu-Mihet method derived from an alternative FPT, and provide a class of stochastic matrix control functions in matrix MB-algebras. Additionally, we estimate permuting trihomomorphisms and permuting tri-derivations in unital matrix MC-lozenge-algebras and matrix MB-algebras.
INTERNATIONAL JOURNAL OF GENERAL SYSTEMS
(2022)
Article
Mathematics
Janusz Brzdek
Summary: This article demonstrates the usage of Banach limit to derive a fixed point theorem for function spaces, and presents its applications in Ulam stability.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2022)
Article
Mathematics, Applied
Arumugam Ponmana Selvan et al.
Summary: This paper aims to establish the Hyers-Ulam stability and hyperstability of a Jensen-type quadratic mapping in 2-Banach spaces. The study proves the various types of stability and hyperstability of the Jensen-type quadratic functional equation in 2-Banach spaces by using the Hyers direct method.
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2022)
Article
Mathematics
Lama Sh. Aljoufi et al.
Summary: In this paper, we investigate the behavior of solutions of a difference equation, including boundedness, stability, and oscillation. The equation has arbitrary non-negative real numbers as initial conditions and a parameter alpha that is greater than or equal to 1.
JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS
(2022)
Article
Mathematics, Applied
Yixing Liang et al.
Summary: This paper discusses the exact solutions of linear homogeneous and nonhomogeneous fractional differential equations with double delays. A new concept of double-delayed Mittag-Leffler type matrix function is introduced, and it is applied along with Laplace transform approach to obtain the exact solutions. The solutions are also used to investigate the Hyers-Ulam stability of the system, and an example is provided to illustrate the techniques.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2022)
Article
Engineering, Multidisciplinary
Safoura Rezaei Aderyani et al.
Alexandria Engineering Journal
(2022)
Article
Computer Science, Artificial Intelligence
Shenglong Chen et al.
Summary: This paper investigates discrete-time fractional-order delayed quaternion-valued neural networks (DFDQNNs) using the direct quaternion approach. A novel lemma and its corresponding corollaries are proposed for estimating the nabla fractional difference of the quaternion-valued Lyapunov function. The existence and uniqueness of equilibrium point for DFDQNNs are proved by constructing a new quaternion-valued contraction mapping. Sufficient criteria for global Mittag-Leffler stability and Mittag-Leffler synchronization of DFDQNNs are obtained using designed Lyapunov functions, effective feedback controller, and neoteric nabla difference inequalities. Numerical examples are provided to verify the results.
Article
Mathematics
M. Youssef
Summary: This paper investigates the solvability of a general class of fractional delay functional equations subject to an infinite point non-classical condition and the Riemann-Stieltjes integral condition. It explores the existence of solutions and the continuous dependence of solutions in three different cases. Illustrative examples are provided to support the results. This work extends some recent developments in the field.
JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS
(2022)
Article
Dhiraj Kumar Singh et al.
Journal of Nonlinear Sciences and Applications
(2020)
Article
Mathematics
S. Karthikeyan et al.
JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS
(2020)
Article
Mathematics, Applied
Janusz Brzdek et al.
BANACH JOURNAL OF MATHEMATICAL ANALYSIS
(2015)
Article
Mathematics, Applied
Justyna Sikorska
AEQUATIONES MATHEMATICAE
(2015)
Review
Mathematics, Applied
Janusz Brzdek et al.
ABSTRACT AND APPLIED ANALYSIS
(2013)
Editorial Material
Mathematics, Applied
Janusz Brzdek et al.
ABSTRACT AND APPLIED ANALYSIS
(2012)
Article
Mathematics, Applied
Wlodzimierz Fechner et al.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2012)
Article
Mathematics, Applied
Dorel Mihet et al.
APPLIED MATHEMATICS LETTERS
(2011)
Article
Mathematics, Applied
Choonkil Park et al.
APPLIED MATHEMATICS LETTERS
(2011)
Article
Mathematics
Jae-Hyeong Bae et al.
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
(2010)
Article
Mathematics, Applied
Jacek Tabor et al.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2007)
