Axioms, Volume 12, Issue 9 (September 2023) – 100 articles

This paper provides both analytical and numerical solutions of (PDEs) involving time-fractional derivatives. We implemented three powerful techniques, including the modified variational iteration technique, the modified Adomian decomposition technique, and the modified homotopy analysis technique, to obtain an approximate solution for the bounded space variable $\nu$. The Laplace transformation is used in the time-fractional derivative operator to enhance the proposed numerical methods’ performance and accuracy and find an approximate solution to time-fractional Fornberg–Whitham equations. To confirm the accuracy of the proposed methods, we evaluate homogeneous time-fractional Fornberg–Whitham equations in terms of non-integer order and variable coefficients. The obtained results of the modified methods are shown through tables and graphs. Full article

Efficient logistics and transport at the port heavily relies on efficient AGV scheduling and planning for container transshipment. This paper presents a comprehensive approach to address the challenges in AGV path planning and coordination within the domain of intelligent transportation systems. We propose an enhanced graph search method for constructing the global path of a single AGV that mitigates the issues associated with paths closely aligned with obstacle corner points. Moreover, a centralized global planning module is developed to facilitate planning and scheduling. Each individual AGV establishes real-time communication with the upper layers to accurately determine its position at complex intersections. By computing its priority sequence within a coordination circle, the AGV effectively treats the high-priority trajectories of other vehicles as dynamic obstacles for its local trajectory planning. The feasibility of trajectory information is ensured by solving the online real-time Optimal Control Problem (OCP). In the trajectory planning process for a single AGV, we incorporate a linear programming-based obstacle avoidance strategy. This strategy transforms the obstacle avoidance optimization problem into trajectory planning constraints using Karush-Kuhn-Tucker (KKT) conditions. Consequently, seamless and secure AGV movement within the port environment is guaranteed. The global planning module encompasses a global regulatory mechanism that provides each AGV with an initial feasible path. This approach not only facilitates complexity decomposition for large-scale problems, but also maintains path feasibility through continuous real-time communication with the upper layers during AGV travel. A key advantage of our progressive solution lies in its flexibility and scalability. This approach readily accommodates extensions based on the original problem and allows adjustments in the overall problem size in response to varying port cargo throughput, all without requiring a complete system overhaul. Full article

This paper explores the cumulative entropy of the lifetime of an n-component coherent system, given the precondition that all system components have experienced failure at time t. This investigation utilizes the system signature to compute the cumulative entropy of the system’s lifetime, shedding light on a crucial facet of a system’s predictability. In the course of this research, we unearth a series of noteworthy discoveries. These include formulating expressions, defining bounds, and identifying orderings related to this measure. Further, we propose a technique to identify a preferred system on the basis of cumulative Kullback–Leibler discriminating information, which exhibits a strong relation with the parallel system. These findings contribute significantly to our understanding of the predictability of a coherent system’s lifetime, underscoring the importance of this field of study. The outcomes offer potential benefits for a wide range of applications where system predictability is paramount, and where the comparative evaluation of different systems on the basis of discriminating information is needed. Full article

In this article, we develop an efficient numerical scheme for dealing with fractional partial integro-differential equations (FPIEs) with a weakly singular kernel. The weight and shift Grünwald difference (WSGD) operator is adopted to approximate a time fractional derivative and the Sinc collocation method is applied for discretizing the spatial derivative.The exponential convergence of our proposed method is demonstrated in detail. Finally, numerical evidence is employed to verify the theoretical results and confirm the expected convergence rate. Full article

We discuss the weighted complementarity problem, extending the nonlinear complementarity problem on $R^n$. In contrast to the NCP, many equilibrium problems in science, engineering, and economics can be transformed into WCPs for more efficient methods. Smoothing Newton algorithms, known for their at least locally superlinear convergence properties, have been widely applied to solve WCPs. We suggest a two-step Newton approach with a local biquadratic order convergence rate to solve the WCP. The new method needs to calculate two Newton equations at each iteration. We also insert a new term, which is of crucial importance for the local biquadratic convergence properties when solving the Newton equation. We demonstrate that the solution to the WCP is the accumulation point of the iterative sequence produced by the approach. We further demonstrate that the algorithm possesses local biquadratic convergence properties. Numerical results indicate the method to be practical and efficient. Full article

This article is devoted to investigating the fixed point theorems for a new contracitivity contraction, which combines the idea involved in Boyd-Wong contractions, strict almost contractions and relational contractions. Our results improve and expand existing fixed point theorems of literature. In process, we deduce a metrical fixed point theorem for strict almost Boyd-Wong contractions. To demonstrate the credibility of our results, we present a number of a few examples. Applying our findings, we find a unique solution to a particular periodic boundary value problem. Full article

This paper proposes new existence and uniqueness results for an initial value problem (IVP) of fractional differential equations of nonlinear variable order. Riemann–Liouville-type fractional derivatives are considered in the problem. The new fundamental results achieved in this work are obtained by using the inequalities technique and the fixed point theory. In addition, uniform stability criteria for the solutions are derived. The accomplished results are new and complement the scientific research in the field. A numerical example is composed to show the efficacy and potency of the proposed criteria. Full article

As a new member of the NA (negative associated) family, the m-AANA (m-asymptotically almost negatively associated) sequence has many statistical properties that have not been developed. This paper mainly studies its properties in the gradual change point model. Firstly, we propose a least squares type change point estimator, then derive the convergence rates and consistency of the estimator, and provide the limit distributions of the estimator. It is interesting that the convergence rates of the estimator are the same as that of the change point estimator for independent identically distributed observations. Finally, the effectiveness of the estimator in limited samples can be verified through several sets of simulation experiments and an actual hydrological example. Full article

Large values and gradients of stress and strain, triggering concentrated stress and strain, arise in angular areas of a structure. The strain action, leading to the finite loss of contact between structural elements, also triggers concentrated stress. The loss of contact reaches an irregular point and a line on the boundary. The theoretical analysis of the stress–strain state (SSS) of areas with angular cutouts in the boundary under the action of discontinuous strain is reduced to the study of singular solutions to the homogeneous problem of elasticity theory with power-related features. The calculation of stress concentration coefficients in the domain of a singular solution to the elastic problem makes no sense. It is experimentally proven that the area located near the vertex of an angular cutout in the boundary features substantial strain and rotations, and it corresponds to higher values of the first and second derivatives of displacements along the radius in cases of sufficiently small radii in the neighborhood of an irregular boundary point. As far as these areas are concerned, it is necessary to consider the plane problem of the elasticity theory, taking into account the geometric nonlinearity under the action of strain, to analyze the effect of relationships between strain orders, rotations, and strain on the form of the equation of equilibrium. The purpose of this work is to analyze the effect of relationships between strain orders, rotations, and strain on the form of the equilibrium equation in the polar system of coordinates for a V-shaped area under the action of temperature-induced strain, taking into account geometric non-linearity and physical linearity. Full article

During the underground mining of coal resources, the rock pressure emerges acutely and the mine geological disasters occur frequently. It is of great significance to grasp the manifestation law of rock pressure in time to guide the safety production and operation in the pit. In this research, the calculation equations and concept of information entropy based on zone safety degree are primarily defined, and the synergetic theory of the maximum information entropy principle is combined to put forward the synergy prediction model of information entropy based on zone safety degree. In the meantime, the synergy prediction model of information entropy based on zone safety degree is employed to calculate and predict the first weighting step and the periodic weighting step of the main roof of the 9203 working face of Hengsheng Coal Mine in China’s Shanxi Province, as well as verifying the validity and reliability of the synergy prediction model of information entropy based on zone safety degree by the comparison of similar simulation test results, which has presented a scientific basis for the effective control of rock pressure and roof management. Full article

A computational approach with the aid of the Linear Multistep Method (LMM) for the numerical solution of differential equations with initial value problems or boundary conditions has appeared several times in the literature due to its good accuracy and stability properties. The major objective of this article is to extend a multistep approach for the numerical solution of the Partial Differential Equation (PDE) originating from fluid mechanics in a two-dimensional space with initial and boundary conditions, as a result of the importance and utility of the models of partial differential equations in applications, particularly in physical phenomena, such as in convection-diffusion models, and fluid flow problems. Thus, a multistep collocation formula, which is based on orthogonal polynomials is proposed. Ninth-order Multistep Collocation Formulas (NMCFs) were formulated through the principle of interpolation and collocation processes. The theoretical analysis of the NMCFs reveals that they have algebraic order nine, are zero-stable, consistent, and, thus, convergent. The implementation strategies of the NMCFs are comprehensively discussed. Some numerical test problems were presented to evaluate the efficacy and applicability of the proposed formulas. Comparisons with other methods were also presented to demonstrate the new formulas’ productivity. Finally, figures were presented to illustrate the behavior of the numerical examples. Full article

Survey sampling has a wide range of applications in biomedical, meteorological, stock exchange, marketing, and agricultural research based on data collected through sample surveys or experimentation. The collected set of information may have a fuzzy nature, be indeterminate, and be summarized by a fuzzy number rather than a crisp value. The neutrosophic statistics, a generalization of fuzzy statistics and classical statistics, deals with the data that have some degree of indeterminacy, imprecision, and fuzziness. In this article, we introduce a fuzzy decision-making approach for deciding a sample size under a fuzzy measurement cost modeled by an intuitionistic fuzzy cost function. Our research introduces neutrosophic ratio-type estimators for estimating the population mean of the neutrosophic study variable $Y_N\in [Y_L,Y_U]$ utilizing all the indeterminate values of the neutrosophic auxiliary variable $X_N\in [X_L,X_U]$ rather than only the extreme values $X_L$ and $X_U$. Three simulation studies are carried out to explain the proposed methods of parameter estimation, sample size determination, and efficiency comparison. The results reveal that the proposed neutrosophic class of estimators produces more accurate and precise estimates of the neutrosophic population mean than the existing neutrosophic estimators in simple random sampling, which is the ultimate goal of inferential statistics. Full article

In this article, the exact solutions of the stochastic conformable Broer–Kaup equations with conformable derivatives which describe the bidirectional propagation of long waves in shallow water are obtained using the modified exponential function method and the generalized Kudryashov method. These exact solutions consist of hyperbolic, trigonometric, rational trigonometric, rational hyperbolic, and rational function solutions, respectively. This shows that the proposed methods are competent and sufficient. In addition, it is aimed to better understand the physical properties by drawing two- and three-dimensional graphics of the exact solutions according to different parameter values. When these exact solutions obtained by two different methods are compared with the solutions attained by other methods, it can be said that these two methods are competent. Full article

This work uses the collocation approximation method to solve a specific type of backward stochastic Volterra integral equations (BSVIEs). Using Newton’s method, BSVIEs can be solved using block pulse functions and the corresponding stochastic operational matrix of integration. We present examples to illustrate the estimate analysis and to demonstrate the convergence of the two approximating sequences separately. To measure their accuracy, we compare the solutions with values of exact and approximative solutions at a few selected locations using a specified absolute error. We also propose an efficient method for solving a triangular linear algebraic problem using a single integral equation. To confirm the effectiveness of our method, we conduct numerical experiments with issues from real-world applications. Full article

Entropy and extropy are emerging concepts in machine learning and computer science. Within the past decade, statisticians have created estimators for these measures. However, associated variability metrics, specifically varentropy and varextropy, have received comparably less attention. This paper presents a novel methodology for computing varentropy and varextropy, drawing inspiration from Bayesian nonparametric methods. We implement this approach using a computational algorithm in R and demonstrate its effectiveness across various examples. Furthermore, these new estimators are applied to test uniformity in data. Full article

The primary intent of this study is to establish some important inequalities of the Hermite–Hadamard, trapezoid, and midpoint types under fractional extended Riemann–Liouville integrals (FERLIs). The proofs are constructed using the renowned Jensen–Mercer, power-mean, and Holder inequalities. Various equalities for the FERLIs and convex functions are construed to be the mainstay for finding new results. Some connections between our main findings and previous research on Riemann–Liouville fractional integrals and FERLIs are also discussed. Moreover, a number of examples are featured, with graphical representations to illustrate and validate the accuracy of the new findings. Full article

In the recent era of research developments, mathematical inequalities and their applications perform a very consequential role in different aspects, and they provide an engaging area for research activities. In this paper, we propose a new approach for the improvement of the classical majorization inequality and its weighted versions in a discrete sense. The proposed improvements give several estimates for the majorization differences. Some earlier improvements of the Jensen and Slater inequalities are deduced as direct consequences of the obtained results. We also discuss the conditions under which the main results give better estimates for the majorization differences. Applications of the acquired results are also presented in information theory. Full article

Bland–Altman limits of agreement are very popular in method comparison studies on quantitative outcomes. However, a straightforward application of Bland–Altman analysis requires roughly normally distributed differences, a constant bias, and variance homogeneity across the measurement range. If one or more assumptions are violated, a variance-stabilizing transformation (e.g., natural logarithm, square root) may be sufficient before Bland–Altman analysis can be performed. Sometimes, fractional polynomial regression has been used when the choice of variance-stabilizing transformation was unclear and increasing variability in the differences was observed with increasing mean values. In this case, regressing the absolute differences on a function of the average and applying fractional polynomial regression to this end were previously proposed. This review revisits a previous inter-rater agreement analysis on the Agatston score for coronary calcification. We show the inappropriateness of a straightforward Bland–Altman analysis and briefly describe the nonparametric limits of agreement of the original investigation. We demonstrate the application of fractional polynomials, use the Stata packages fp and fp_select, and discuss the use of degree-2 (the default setting) and degree-3 fractional polynomials. Finally, we discuss conditions for evaluating the appropriateness of nonstandard limits of agreement. Full article

The global fixed-time sliding mode control strategy is designed for the manipulator to achieve global fixed-time trajectory tracking in response to the uncertainty of the system model, the external disturbances, and the saturation of the manipulator actuator. First, aiming at the lumped disturbance caused by system model uncertainty and external disturbance, the adaptive fixed-time sliding mode disturbance observer (AFSMDO) was introduced to eliminate the negative effects of disturbance. The observer parameters can adaptively change with disturbances by designing the adaptive law, improving the accuracy of disturbance estimation. Secondly, the fixed-time sliding surface was introduced to avoid singularity, and the nonsingular fixed-time sliding mode control (NFSMC) design was put in place to ensure the global convergence of the manipulator system. Finally, the fixed time saturation compensator (FTSC) was created for NFSMC to prevent the negative impact of actuator saturation on the manipulator system, effectively reducing system chatter and improving the response speed of the closed-loop system. The fixed-time stability theory and Lyapunov method were exploited to offer a thorough and rigorous theoretical analysis and stability demonstration for the overall control system. Simulation experiments verify that the designed control scheme has excellent control effects and strong practicability. Full article

This paper is to study finite horizon linear quadratic (LQ) non-zero sum Nash game for discrete-time infinite Markov jump stochastic systems (IMJSSs). Based on the theory of stochastic analysis, a countably infinite set of coupled generalized algebraic Riccati equations are solved and a necessary and sufficient condition for the existence of Nash equilibrium points is obtained. From a new perspective, the finite horizon mixed robust $H_2/H_{\infty }$ control is investigated, and summarize the relationship between Nash game and $H_2/H_{\infty }$ control problem. Moreover, the feasibility and validity of the proposed method has been proved by applying it to a numerical example. Full article

In this article, we investigate the utilization of Riemann–Liouville’s fractional integral and the Caputo derivative in the application of the Optimal Auxiliary Function Method (OAFM). The extended OAFM is employed to analyze fractional non-linear coupled ITO systems and non-linear KDV systems, which feature equations of a fractional order in time. We compare the results obtained for the ITO system with those derived from the Homotopy Perturbation Method (HPM) and the New Iterative Method (NIM), and for the KDV system with the Laplace Adomian Decomposition Method (LADM). OAFM demonstrates remarkable convergence with a single iteration, rendering it highly effective. In contrast to other existing analytical approaches, OAFM emerges as a dependable and efficient methodology, delivering high-precision solutions for intricate problems while saving both computational resources and time. Our results indicate superior accuracy with OAFM in comparison to HPM, NIM, and LADM. Additionally, we enhance the accuracy of OAFM through the introduction of supplementary auxiliary functions. Full article

In this paper, we consider the one-dimensional Ising model (shortly, 1D-MSIM) having mixed spin-$(s,(2t-1)/2)$ with the nearest neighbors and the external magnetic field. We establish the partition function of the model using the transfer matrix. We compute certain thermodynamic quantities for the 1D-MSIM. We find some precise formulas to determine the model’s free energy, entropy, magnetization, and susceptibility. By examining the iterative equations associated with the model, we use the cavity approach to investigate the phase transition problem. We numerically determine the model’s periodicity. Full article

In this article we consider zeroes for multifunctions with possibly noncompact image sets. We introduce the notion of multifunction with $\mathbb{K}$-inf-compact support. We also establish three types of applications: the Bayesian approach for analysis of financial operational risk under certain constraints, occupational health and safety measures optimization, and transfer of space innovations and technologies. Full article

A stochastic predator–prey system with group cooperative behavior, white noise, and Lévy noise is considered. In group cooperation, we introduce the Holling IV interaction term to reflect group defense of prey, and cooperative hunting to reflect group attack of predator. Firstly, it is proved that the system has a globally unique positive solution. Secondly, we obtain the conditions of persistence and extinction of the system in the sense of time average. Under the condition that the environment does not change dramatically, the intensity of cooperative hunting and group defense needs to meet certain conditions to make both predators and preys persist. In addition, considering the system without Lévy jump, it is proved that the system has a stationary distribution. Finally, the validity of the theoretical results is verified by numerical simulation. Full article

The objective of this paper is to study the hybrid near algebra. It has been summarized with the proper definitions and theorems of hybrid near algebra, hybrid near algebra homomorphism and direct product of hybrid near algebra. It has been proved that a homomorphic image of a hybrid near algebra is a hybrid near algebra. It also investigated the intersection of two hybrid near algebras is a hybrid near algebra. Full article

This study investigates the oscillatory properties of a fourth-order delay functional differential equation. This study’s methodology is built around two key tenets. First, we propose optimized relationships between the solution and its derivatives by making use of some improved monotonic features. By using a comparison technique to connect the oscillation of the studied equation with some second-order equations, the second aspect takes advantage of the significant progress made in the study of the oscillation of second-order equations. Numerous applications of functional differential equations of the neutral type served as the inspiration for the study of a subclass of these equations. Full article

We obtain the separability of mixed-norm Herz-slice spaces, establish a weak convergence on mixed-norm Herz-slice spaces, and get the boundedness of the Calderón–Zygmund operator T on mixed-norm Herz-slice spaces. Moreover, we get the necessary and sufficient conditions for the boundedness of the commutator $[b,T]$ on mixed-norm Herz-slice spaces, where b is a locally integrable function. Full article

Typhoons often cause huge losses, so it is significant to accurately predict typhoon tracks. Nowadays, researchers predict typhoon tracks with the single step, while the correlation of adjacent moments data is small in long-term prediction, due to the large step of time. Moreover, recursive multi-step prediction results in the accumulated error. Therefore, this paper proposes to fuse reanalysis images at the similarly historical moment and predicted images through Laplacian Pyramid and Discrete Wavelet Transform to reduce the accumulated error. That moment is determined according to the difference in the moving angle at predicted and historical moments, the color histogram similarity between predicted images and reanalysis images at historical moments and so on. Moreover, reanalysis images are weighted cascaded and input to ConvLSTM on the basis of the correlation between reanalysis data and the moving angle and distance of the typhoon. And, the Spatial Attention and weighted calculation of memory cells are added to improve the performance of ConvLSTM. This paper predicted typhoon tracks in 12 h, 18 h, 24 h and 48 h with recursive multi-step prediction. Their MAEs were 102.14 km, 168.17 km, 243.73 km and 574.62 km, respectively, which were reduced by 1.65 km, 5.93 km, 4.6 km and 13.09 km, respectively, compared with the predicted results of the improved ConvLSTM in this paper, which proved the validity of the model. Full article

In veins, clotting initiation displays a threshold response to flow intensity and injury size. Mathematical models can provide insights into the conditions leading to clot growth initiation under flow for specific subjects. However, it is hard to determine the thrombin generation curves that favor coagulation initiation in a fast manner, especially when considering a wide range of conditions related to flow and injury size. In this work, we propose to address this challenge by using a neural network model trained with the numerical simulations of a validated 2D model for clot formation. Our surrogate model approximates the results of the 2D simulations, reaching an accuracy of 94% on the test dataset. We used the trained artificial neural network to determine the threshold for thrombin generation parameters that alter the coagulation initiation response under varying flow speed and injury size conditions. Our model predictions show that increased levels of the endogenous thrombin potential (ETP) and peak thrombin concentration increase the likelihood of coagulation initiation, while an elevated time to peak decreases coagulation. The lag time has a small effect on coagulation initiation, especially when the injury size is small. Our surrogate model can be considered as a proof-of-concept of a tool that can be deployed to estimate the risk of bleeding in specific patients based on their Thrombin Generation Assay results. Full article

This study addresses the issue of estimating the shape parameter of the inverted exponentiated Rayleigh distribution, along with the assessment of reliability and failure rate, by utilizing Type-I progressive hybrid censored data. The study explores the estimators based on maximum likelihood, Bayes, and empirical Bayes methodologies. Additionally, the study focuses on the development of Bayes and empirical Bayes estimators with balanced loss functions. A concrete example based on actual data from the field of medicine is used to illustrate the theoretical insights provided in this study. Monte Carlo simulations are employed to conduct numerical comparisons and evaluate the performance and accuracy of the estimation methods. Full article