Axioms

38 pages, 479 KB

Open AccessArticle

Existence and Uniqueness of Solutions for Singular Fractional Integro-Differential Equations with p-Laplacian and Two Kinds of Fractional Derivatives

by Fang Wang, Lishan Liu, Haibo Gu, Lina Ma and Yonghong Wu

Axioms 2025, 14(12), 890; https://doi.org/10.3390/axioms14120890 (registering DOI) - 30 Nov 2025

Abstract

The paper is devoted to the study of a class of singular high-order fractional integro-differential equations with p-Laplacian operator, involving both the Riemann–Liouville fractional derivative and the Caputo fractional derivative. First, we investigate the problem by the method of reducing the order [...] Read more.

The paper is devoted to the study of a class of singular high-order fractional integro-differential equations with p-Laplacian operator, involving both the Riemann–Liouville fractional derivative and the Caputo fractional derivative. First, we investigate the problem by the method of reducing the order of fractional derivative. Then, by using the Schauder fixed point theorem, the existence of solutions is proved. The upper and lower bounds for the unique solution of the problem are established under various conditions by employing the Banach contraction mapping principle. Furthermore, four numerical examples are presented to illustrate the applications of our main results. Full article

(This article belongs to the Topic Fractional Calculus: Theory and Applications, 2nd Edition)

17 pages, 333 KB

Open AccessArticle

Common Fixed Point Approximation for Asymptotically Nonexpansive Mapping in Hyperbolic Space with Application

by Tehreem Ishtiaq, Afshan Batool, Aftab Hussain and Hamed Alsulami

Axioms 2025, 14(12), 889; https://doi.org/10.3390/axioms14120889 (registering DOI) - 30 Nov 2025

Abstract

This study presents a common fixed-point iteration process that includes two asymptotically nonexpansive self-mappings in a hyperbolic space and their delta convergence. To support our results, we provide an example with a comparison table and sufficient conditions for a modified iteration scheme to [...] Read more.

This study presents a common fixed-point iteration process that includes two asymptotically nonexpansive self-mappings in a hyperbolic space and their delta convergence. To support our results, we provide an example with a comparison table and sufficient conditions for a modified iteration scheme to have strong convergence to approximate the fixed point. Full article

(This article belongs to the Special Issue Recent Advances in Special Functions and Applications, 2nd Edition)

26 pages, 1043 KB

Open AccessArticle

Global Existence and Large-Time Behavior for 3D Full Compressible Magneto-Micropolar System Without Heat Conductivity

by Yuxiao Pan, Heyu Wang and Mingyu Zhang

Axioms 2025, 14(12), 888; https://doi.org/10.3390/axioms14120888 (registering DOI) - 30 Nov 2025

Abstract

The system of full compressible magneto-micropolar flows is discussed in 3D bounded domains with slip boundary conditions. Based on the energy method, after establishing some key a priori exponential decay-in-times rates of the strong solutions, we obtain both the global existence and exponential [...] Read more.

The system of full compressible magneto-micropolar flows is discussed in 3D bounded domains with slip boundary conditions. Based on the energy method, after establishing some key a priori exponential decay-in-times rates of the strong solutions, we obtain both the global existence and exponential stability of strong solutions. In particular, it should be pointed out that the estimates of

{∥ (curl u, curl w) ∥}_{L^{2}}

and

{∥ (div u, div w) ∥}_{L^{2}}

are established separately, which implies that the growth rate of

(div u, div w)

in

L^{2}

are faster than that of

(curl u, curl w)

under the condition that the diameter of the domain is suitably large. Compared with previous works, we no longer consider the pressure P as

ρ θ

, but as variable in

(x, t)

, and directly deal with

{∥ \nabla P ∥}_{L^{2}}

. Based on slip boundary conditions, we established the

L^{p}

-norm for the gradient of effective viscous flux, and the term

{∥ \nabla P ∥}_{L^{2}}

can be controlled by

∥ (\nabla u_{t}, \nabla w_{t}, \nabla b_{t}) ∥_{L^{2}}

. Through precise calculations, we found that

∥ (\nabla u_{t}, \nabla w_{t}, \nabla b_{t}) ∥_{L^{2}}

is dependent on

{∥ \nabla P ∥}_{L^{2}}

. Therefore, the smallness condition we propose does not depend on the

L^{r}

-norm of the density gradient, which means that density can contain large oscillations. Full article

(This article belongs to the Section Mathematical Physics)

20 pages, 1287 KB

Open AccessArticle

GrImp: Granular Imputation of Missing Data for Interpretable Fuzzy Models

by Krzysztof Siminski and Konrad Wnuk

Axioms 2025, 14(12), 887; https://doi.org/10.3390/axioms14120887 (registering DOI) - 30 Nov 2025

Abstract

Data incompleteness is a common problem in real-life datasets. This is caused by acquisition problems, sensor failures, human errors, and so on. Missing values and their subsequent imputation can significantly affect the performance of data-driven models and can also distort the interpretability of [...] Read more.

Data incompleteness is a common problem in real-life datasets. This is caused by acquisition problems, sensor failures, human errors, and so on. Missing values and their subsequent imputation can significantly affect the performance of data-driven models and can also distort the interpretability of explainable artificial intelligence (XAI) models, such as fuzzy models. This paper presents a novel imputation algorithm based on granular computing. This method benefits from the local structure of the dataset, explored using the granular approach. The method elaborates a set of granules that are then used to impute missing values in the dataset. The method is evaluated on several datasets and compared with several state-of-the-art imputation methods, both directly and indirectly. The direct evaluation compares the imputed values with the original data. The indirect evaluation compares the performance of fuzzy models built with TSK and ANNBFIS neuro-fuzzy systems. This enables not only the evaluation of the quality of numerically imputed values but also their impact on the interpretability of the constructed fuzzy models. This paper is accompanied by numerical experiments. The implementation of the method is available in a public GitHub repository. Full article

(This article belongs to the Special Issue Advances in Fuzzy Logic and Fuzzy Implications)

29 pages, 387 KB

Open AccessArticle

New Approach for Closure Spaces on Graphs Based on Relations and Graph Ideals

by Rehab Alharbi, S. E. Abbas, H. M. Khiamy and Ismail Ibedou

Axioms 2025, 14(12), 886; https://doi.org/10.3390/axioms14120886 (registering DOI) - 29 Nov 2025

Abstract

The main aim of this paper is to combine the connections between graph theory and rough set theory. We created graph ideal ASs by proposing the interior and closure operators, utilizing the concept of graph ideals. With the help of various graphical examples, [...] Read more.

The main aim of this paper is to combine the connections between graph theory and rough set theory. We created graph ideal ASs by proposing the interior and closure operators, utilizing the concept of graph ideals. With the help of various graphical examples, we applied some topological concepts to the induced graph ideal ASs, including the subspace, continuous functions, lower separation axioms, and connectedness. However, simple directed graphs with or without loops are the ones that are discussed throughout the study. The obtained results are valid for any type of graph: multi-graphs or simple graphs, connected or disconnected graphs, with loops or without loops, and undirected or directed graphs. Full article

(This article belongs to the Section Geometry and Topology)

19 pages, 1118 KB

Open AccessArticle

Synchronization of Networked Reaction-Diffusion Nonlinear Systems via Hybrid Control

by Dongfang Mao, Guoping Jiang, Qian Ye and Meilin Chen

Axioms 2025, 14(12), 885; https://doi.org/10.3390/axioms14120885 (registering DOI) - 29 Nov 2025

Abstract

This paper addresses the asymptotic synchronization problem for networked nonlinear reaction–diffusion systems under a novel hybrid control strategy. The hybrid controller consists of two components: impulsive control and continuous feedback control. By combining the comparison principle of impulsive systems with the introduction of [...] Read more.

This paper addresses the asymptotic synchronization problem for networked nonlinear reaction–diffusion systems under a novel hybrid control strategy. The hybrid controller consists of two components: impulsive control and continuous feedback control. By combining the comparison principle of impulsive systems with the introduction of a time-varying function and a power exponent to flexibly adjust the system, sufficient conditions for synchronization of networked nonlinear reaction–diffusion systems are derived, ensuring that the error dynamics between the network nodes converge to zero. Numerical simulations of a representative example are presented to demonstrate the practical validity and effectiveness of the proposed theoretical control scheme, confirming that the hybrid controller successfully achieves synchronization. Full article

20 pages, 680 KB

Open AccessArticle

Parameter Estimation for Stochastic Korteweg–de Vries Equations

by Zhenyu Lang, Xiuling Yin, Yanqin Liu and Yaru Wang

Axioms 2025, 14(12), 884; https://doi.org/10.3390/axioms14120884 (registering DOI) - 29 Nov 2025

Abstract

In this paper, we propose two methods for parameter estimation in stochastic Korteweg–de Vries (KdV) equations with unknown parameters. Both methods are based on the numerical discretization of the stochastic KdV equation. Moreover, we further propose an extrapolation-based approach to improve the accuracy [...] Read more.

In this paper, we propose two methods for parameter estimation in stochastic Korteweg–de Vries (KdV) equations with unknown parameters. Both methods are based on the numerical discretization of the stochastic KdV equation. Moreover, we further propose an extrapolation-based approach to improve the accuracy of parameter estimation. In addition, for the deterministic case, the convergence and conservation of the fully discrete schemes are analyzed. Both our theoretical analysis and numerical tests indicate the efficiency of the proposed methods for the KdV equations considered. Full article

(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics, 2nd Edition)

20 pages, 609 KB

Open AccessArticle

Geometric Fusion Mechanism for Reliable Central Measure Construction Amid Partial and Distorted Information

by Mohammed Ahmed Alomair and Muhammad Raza

Axioms 2025, 14(12), 883; https://doi.org/10.3390/axioms14120883 (registering DOI) - 29 Nov 2025

Abstract

Biased estimates and fluctuating measures of central tendency are significant impediments to statistical inference and computational data analysis and are often caused by partial and distorted observations. The imputed least-squares-based estimators are very sensitive to non-normality, outliers, and missing data; thus, they cannot [...] Read more.

Biased estimates and fluctuating measures of central tendency are significant impediments to statistical inference and computational data analysis and are often caused by partial and distorted observations. The imputed least-squares-based estimators are very sensitive to non-normality, outliers, and missing data; thus, they cannot guarantee reliability in the presence of anomalous data. In an attempt to overcome these inadequacies, this paper utilizes a geometric fusion scheme, the Minimum Regularized Covariance Determinant (MRCD), to construct high-quality central measures. The suggested mechanism incorporates the concept of geometric dispersion and resistance-based principles of covariance to form stable dispersion structures, irrespective of data contamination and incompleteness. In this computational scheme, three estimators are developed, all of which use adaptive logarithmic transformations to boost efficiency and robustness. The theoretical argument can be characterized by analytical derivations of bias and Mean Squared Error (MSE) in large-sample situations, and empirical gains were verified by large-scale Monte Carlo experiments using synthetic populations and real-world datasets. The proposed MRCDdriven estimators are known to have a lower MSE as well as higher percentage relative efficiency (PRE) as compared to classical estimators. Overall, the findings indicate that the geometric fusion mechanism (MRCD) is a powerful, self-scaling, and statistically sound way of computing central measures in a situation in which information is incomplete and distorted. Full article

(This article belongs to the Section Mathematical Analysis)

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11 pages, 1298 KB

Open AccessArticle

A Modified Auxiliary Method for Efficient Solutions to the (2+1)-Dimensional Variable-Coefficient Burgers’ Equation

by Yiman Han and Yanni Zhang

Axioms 2025, 14(12), 882; https://doi.org/10.3390/axioms14120882 (registering DOI) - 29 Nov 2025

Abstract

This paper explores an innovative expansion method for solving variable-coefficient partial differential equations. Combining specific auxiliary equations with the aid of mathematical software, our method achieves notable perspectives for understanding and solving related physical problems. The validity of this method was verified through [...] Read more.

This paper explores an innovative expansion method for solving variable-coefficient partial differential equations. Combining specific auxiliary equations with the aid of mathematical software, our method achieves notable perspectives for understanding and solving related physical problems. The validity of this method was verified through the (2+1)-dimensional variable-coefficient Burgers’ equation, and the results were visualized using three-dimensional surface plots. This study proposes an effective method for solving partial differential equations that holds broad application prospects in the field of fluid physics. Full article

(This article belongs to the Topic Functional Equations: Methods and Applications)

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21 pages, 1283 KB

Open AccessArticle

Modified Tseng’s Extragradient Method for Solving Variational Inequality Problems and Fixed Point Problems with Applications in Optimal Control Problems

by Yaling Bai, Guolin Yu, Linqi Sun and Shengquan Weng

Axioms 2025, 14(12), 881; https://doi.org/10.3390/axioms14120881 (registering DOI) - 28 Nov 2025

Abstract

This paper presents an enhanced inertial Tseng’s extragradient method designed to address variational inequality problems involving pseudomonotone operators, along with fixed point problems governed by quasi-nonexpansive operators in real Hilbert spaces. Provided that the parameters satisfy appropriate conditions, the proposed method is shown [...] Read more.

This paper presents an enhanced inertial Tseng’s extragradient method designed to address variational inequality problems involving pseudomonotone operators, along with fixed point problems governed by quasi-nonexpansive operators in real Hilbert spaces. Provided that the parameters satisfy appropriate conditions, the proposed method is shown to converge strongly. Finally, we provide computational results and illustrate their utility through optimal control applications. These aim to show the efficacy and superiority of the proposed algorithm compared with some existing algorithms. Full article

(This article belongs to the Special Issue Mathematics and Its Applications in Other Disciplines)

32 pages, 2759 KB

Open AccessArticle

Convergence-Enhanced and ANN-Accelerated Solvers for Absolute Value Problems

by Mudassir Shams and Bruno Carpentieri

Axioms 2025, 14(12), 880; https://doi.org/10.3390/axioms14120880 (registering DOI) - 28 Nov 2025

Abstract

Absolute value problems of the form

A x - | x | = b

, where

x \in R^{n}

is the unknown vector,

b \in R^{n}

is a given vector, and

A \in R^{n \times n}

is a matrix, arise [...] Read more.

Absolute value problems of the form

A x - | x | = b

, where

x \in R^{n}

is the unknown vector,

b \in R^{n}

is a given vector, and

A \in R^{n \times n}

is a matrix, arise in a wide range of scientific and engineering applications. Their solution is challenging due to the non-differentiability of the absolute value operator and the possible existence of multiple solutions. Classical iterative techniques often suffer from slow convergence, strong sensitivity to the choice of initial vectors, and limited global convergence guarantees. In this study, we introduce a novel two-step iterative scheme that incorporates an adaptive initialization strategy enhanced by artificial neural networks (ANNs). The proposed method attains global linear convergence and local third-order convergence, thereby combining robustness with high accuracy. Numerical experiments on a range of benchmark problems—including cases with both unique and multiple solutions—demonstrate that the ANN-assisted initialization substantially accelerates convergence. In particular, it reduces the number of iterations, computational time, and residual errors across multiple norms, including both the Euclidean and infinity norms. These findings demonstrate that coupling a high-order two-step solver with ANN-based adaptive initialization yields a reliable and efficient framework for solving absolute value problems in both theoretical analysis and practical large-scale applications. Full article

25 pages, 760 KB

Open AccessArticle

A Higher-Order Ising Model with Gradient-Free Update

by Gengsheng L. Zeng

Axioms 2025, 14(12), 879; https://doi.org/10.3390/axioms14120879 (registering DOI) - 28 Nov 2025

Abstract

The Ising model is able to memorize some patterns or solutions as stable states. An Ising network may automatically converge to a pre-stored solution for a random input. However, in many cases, the Ising model cannot perform this task. The gap is that [...] Read more.

The Ising model is able to memorize some patterns or solutions as stable states. An Ising network may automatically converge to a pre-stored solution for a random input. However, in many cases, the Ising model cannot perform this task. The gap is that for a set of desired patterns, one may not be able to construct an Ising model such that the desired patterns are the stable solutions of the Ising model. The Ising model has limited power, because its energy function is limited to a second-order polynomial. Our research outline is as follows. This paper extends the conventional Ising model so that it has wider applications, where the Hebbian rule no longer works. The extended model does not have a limit on the order of the energy function. The extended Ising is defined by combining all desired patterns in a product. Our findings are that the extended Ising model has explicit closed-from update formulas, which do not require the evaluation of gradients. Thus, no network training is necessary. The update algorithm takes finite steps to reach a local minimum. Full article

18 pages, 302 KB

Open AccessArticle

On Non-Archimedean Fuzzy Metric Free Topological Groups

by Cristina Bors and Manuel Sanchis

Axioms 2025, 14(12), 878; https://doi.org/10.3390/axioms14120878 (registering DOI) - 28 Nov 2025

Abstract

We construct the free group over a non-Archimedean fuzzy metric space

(X, M, \land)

in the sense of George and Veeramani where ∧ is the minimum t-norm. The two main tools used are the concept of a scheme [...] Read more.

We construct the free group over a non-Archimedean fuzzy metric space

(X, M, \land)

in the sense of George and Veeramani where ∧ is the minimum t-norm. The two main tools used are the concept of a scheme (for every non-empty subset S of

N

of even cardinal, a permutation

φ

on S is a scheme for S if it is idempotent, with no fixed points and, additionally,

i < j < φ (i) < φ (j)

does not hold for every

i, j \in S

), and the notion of a fuzzy prenorm on a fuzzy topological group. As a consequence of our results, we prove that every non-Archimedean fuzzy metric space

(X, M, \land)

in the sense of George and Veeramani is isometric to a closed subspace of a non-Archimedean fuzzy metric free (Abelian) group and also that every metric space

(X, d)

is uniformly isomorphic to a closed subspace of a non-Archimedean fuzzy metric free (Abelian) group. Our results also apply to non-Archimedean fuzzy metric spaces in the sense of Kramosil and Michálek. Full article

18 pages, 1074 KB

Open AccessArticle

Third-Order Functional Differential Equations with Damping Term: Oscillatory Behavior of Solutions

by Asma Al-Jaser, Eman Alluqmani, Belgees Qaraad and Higinio Ramos

Axioms 2025, 14(12), 877; https://doi.org/10.3390/axioms14120877 (registering DOI) - 28 Nov 2025

Abstract

In this paper, we investigate the asymptotic and oscillatory behavior of a specific class of third-order functional differential equations with damping terms and deviating arguments. By employing the comparison principle, Riccati transformation, and the integral averaging technique, we derive new criteria that guarantee [...] Read more.

In this paper, we investigate the asymptotic and oscillatory behavior of a specific class of third-order functional differential equations with damping terms and deviating arguments. By employing the comparison principle, Riccati transformation, and the integral averaging technique, we derive new criteria that guarantee all solutions to the studied equation oscillate when

\int_{⊤_{0}}^{\infty} 1 / γ^{1 / α} (⊤) d ⊤ = \infty

and

ϱ (⊤) \leq ϱ_{0} < \infty

. This study introduces novel conditions and effective analytical tools, which enhance our understanding of such equations and broaden their range of applications. Illustrative examples are provided to demonstrate the applicability of the results. Full article

(This article belongs to the Special Issue Special Functions and Related Topics, 2nd Edition)

17 pages, 289 KB

Open AccessArticle

Additive Derivations of Incidence Modules

by Naseer Ullah, Hailou Yao, Dalal Alhwikem and Imran Shabir Chuhan

Axioms 2025, 14(12), 876; https://doi.org/10.3390/axioms14120876 (registering DOI) - 28 Nov 2025

Abstract

Let R be an associative ring and M a left R-module. This paper examines the structural properties of the incidence module

I (P, M)

, associated with a module M over a ring R and a locally finite poset [...] Read more.

Let R be an associative ring and M a left R-module. This paper examines the structural properties of the incidence module

I (P, M)

, associated with a module M over a ring R and a locally finite poset

P

. We provide a complete characterization of when an additive derivation on

I (P, M)

is inner, for the case where

P

is a finite and connected poset. These criteria are then generalized to arbitrary posets, revealing a profound connection between the algebraic properties of the module and the graph-theoretic structure of

P

as a directed graph. Full article

14 pages, 725 KB

Open AccessArticle

Estimation for Longitudinal Varying Coefficient Partially Nonlinear Models Based on QR Decomposition

by Jiangcui Ge, Xiaoshuang Zhou and Cuiping Wang

Axioms 2025, 14(12), 875; https://doi.org/10.3390/axioms14120875 - 28 Nov 2025

Abstract

To address the estimation efficiency issues arising from multicollinearity and longitudinal data correlation in the varying coefficient partially nonlinear models (VCPNLM), a method based on QR decomposition and quadratic inference function (QIF) is proposed to obtain the orthogonality estimation of parameter components and [...] Read more.

To address the estimation efficiency issues arising from multicollinearity and longitudinal data correlation in the varying coefficient partially nonlinear models (VCPNLM), a method based on QR decomposition and quadratic inference function (QIF) is proposed to obtain the orthogonality estimation of parameter components and varying coefficient functions. QR decomposition eliminates the pathology of the design matrix, and combines the adaptive weighting of the relevant structures within the group by QIF to effectively capture the complex correlation structure of longitudinal data. The theoretical analysis proves the asymptotic nature of the estimator, and the efficiency of the estimation method proposed in this paper is verified by simulation experiments. Full article

(This article belongs to the Special Issue Computational Statistics and Its Applications, 2nd Edition)

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14 pages, 252 KB

Open AccessArticle

Nonlinear Mixed Jordan-Type Derivations on ∗-Algebra

by Amal S. Alali, Md Arshad Madni and Muzibur Rahman Mozumder

Axioms 2025, 14(12), 874; https://doi.org/10.3390/axioms14120874 - 28 Nov 2025

Abstract

Let

A

be a unital ∗-algebra over the complex fields

C

. In this article, it is proved that a nonlinear mixed bi-skew Jordan n-derivation is an additive ∗-derivation under certain conditions. As applications, the main result is applied to some special [...] Read more.

Let

A

be a unital ∗-algebra over the complex fields

C

. In this article, it is proved that a nonlinear mixed bi-skew Jordan n-derivation is an additive ∗-derivation under certain conditions. As applications, the main result is applied to some special classes of ∗-algebras such as prime ∗-algebra, standard operator algebra, factor von Neumann algebra and von Neumann algebra with no central summands of type

I_{1}

. Full article

(This article belongs to the Section Algebra and Number Theory)

14 pages, 272 KB

Open AccessArticle

Extremality of Koebe’s Function

by Samuel L. Krushkal

Axioms 2025, 14(12), 873; https://doi.org/10.3390/axioms14120873 - 28 Nov 2025

Abstract

The remarkable Koebe function is the (unique) extremal of many important distortion functionals in geometric function theory. This paper provides a complete characterization of such functionals. Full article

(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications, 2nd Edition)

21 pages, 261 KB

Open AccessArticle

On Prime Rings with Derivations

by Khalid H. Al-Shaalan

Axioms 2025, 14(12), 872; https://doi.org/10.3390/axioms14120872 - 27 Nov 2025

Abstract

This paper identifies all derivations associated with two well-known non-commutative prime rings and provides some remarks on one of these derivations, called the prime derivation. Also, it presents two results for some classes of non-commutative prime rings, regarding when the images of derivations [...] Read more.

This paper identifies all derivations associated with two well-known non-commutative prime rings and provides some remarks on one of these derivations, called the prime derivation. Also, it presents two results for some classes of non-commutative prime rings, regarding when the images of derivations on these rings are subrings of them. The paper also includes some illustrative examples and concludes with a set of questions for further exploration of this topic. Full article

(This article belongs to the Section Algebra and Number Theory)

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