Journal of Advances in Applied & Computational Mathematics
The Journal of Advances in Applied & Computational Mathematics is a peer-reviewed publication that serves as a platform for the dissemination of cutting-edge research in the fields of applied mathematics and computational mathematics. The journal is dedicated to advancing the understanding and application of mathematical methods in a wide range of real-world problems and disciplines, including physics, engineering, biology, finance, and more. The journal publishes high-quality, original research articles, review papers, and technical reports that present new methods, algorithms, and models in applied and computational mathematics. The aim of the journal is to provide a comprehensive and up-to-date resource for researchers, academics, and practitioners in these fields, and to promote interdisciplinary collaboration among mathematicians, scientists, and engineers. Whether you are a researcher exploring the frontiers of mathematical theory, or a practitioner looking for new ways to solve real-world problems, the Journal of Advances in Applied & Computational Mathematics is an indispensable resource for staying informed about the latest developments and advancements in these fields. The journal is committed to advancing the understanding and application of mathematical methods for the benefit of society and the scientific community.
All the published articles are licensed under the terms of the Creative Commons Attribution Non-Commercial License (CC BY-NC 4.0) which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.
Equivalence Analysis of Two Different Methods for Solving Fuzzy Linear Systems
In this paper, the distinction and connection between a new approach introduced in [29] and the traditional method presented in [1] for some semi-fuzzy linear systems are discussed. Firstly, the consistency of some primary algebraic operations between the a-center and a–radius of a fuzzy number x~\widetilde{x}x and the a-levels of a fuzzy number x~\widetilde{x}x is analyzed. Secondly, the equivalence property of the computing model and the strong fuzzy solution in recent paper [29] by discussing the proposed method twenty-eight years ago [1] are considered. Then, the dual fuzzy linear systems are also investigated in a similar way. Finally, two classical and well known examples are given to show the validity of the new method in which the idea and approach can be applied to simplifying calculation of any semi-fuzzy linear systems.
Copyright (c) 2025 Yahui Liu, Xinyi Duan, Xiaobin Guo https://creativecommons.org/licenses/by-nc/4.0
Accurate Estimation of COVID-19 Active Cases Using Bézier Curve-Based Mathematical Modeling
COVID-19 has reminded humanity of the devastating reality of a pandemic after many years. This global crisis fundamentally altered daily life and exposed significant vulnerabilities in public health systems worldwide. This work proposes a geometric curve-based prototype to support the fight against current and future pandemics. The study models a near-perfect estimation of the active case number with the help of the Bézier curve. The Bézier prototype consists of a C0 class, piecewise continuous, and segmented structure. The noiseless and cost-free model estimates the number of active cases in Germany, Canada, and Israel with minimum error. It compares the results obtained with those of cases in China. The absolute average error of the model is reduced to 0.087%. As a result, the consistent and cost-effective model can increase the likelihood of making rapid and accurate decisions against epidemics, produce well-organized projections for the future, and improve the effectiveness of measures to be taken.
Copyright (c) 2025 Emre Eroglu https://creativecommons.org/licenses/by-nc/4.0
Normalized Solutions for Biharmonic Equation with Combined Pure-power and Saturable Nonlinearities
We investigate the existence of normalized solutions to the biharmonic equation with combined pure-power and saturable nonlinearities: where 5 < N < 7, 2 < p < 4*: = μ > 0 is a parameter, λ ∈ R arises as a Lagrange multiplier associated with the L2-constraint, and – 1 < g < 0 is a constant. By employing variational methods and analyzing the problem on the Pohozaev manifold, we establish the existence of ground state solutions in the L2-subcritical regime and mountain-pass type solutions in the L2-supercritical regime.
Copyright (c) 2025 Yue Ma, Ziheng Zhang https://creativecommons.org/licenses/by-nc/4.0
Dynamic Bifurcation Analysis of Incommensurate Fractional-Order Hopfield Neural Networks with Multiple Time Delays
This study extends a traditional neural network model to an asymmetric Hopfield model incorporating triple time delays through a combined qualitative and quantitative analytical approach. The system is first linearized using Taylor series expansion, followed by the determination of bifurcation points in the resulting system of equations containing quadratic transcendental terms. An improved Adams-Bashforth-Moulton predictor-corrector method is employed for discretization analysis. Theoretical findings are validated through three numerical case studies, with further examination of how time delays influence the system’s dynamic behavior.
Copyright (c) 2025 Jun Jiang, Yiqing Wang https://creativecommons.org/licenses/by-nc/4.0
Dynamic Event-triggered H∞ State Estimation for Memristive Neural Networks with Variance Constraints and Time-delay: A Finite-horizon Approach
This paper discusses the dynamic event-triggered H∞ state estimation issue for memristive neural networks with time-delay under variance constraints. The dynamic event-triggered mechanism is incorporated into the sensor-to-estimator to reduce resource consumption in the communication channel. The objective is to design the time-varying state estimator such that, in the presence of the dynamic event-triggered mechanism and time-delay, new sufficient criteria are derived to ensure the desired H∞ performance and the boundedness of estimation error variance. Furthermore, a novel non-augmented H∞ state estimation algorithm is proposed under variance constraint by using the stochastic analysis techniques. Finally, a simulation example is used to illustrate the effectiveness of the proposed H∞ state estimation algorithm.
Copyright (c) 2025 Yan Gao, Yan Zhang, Jun Hu https://creativecommons.org/licenses/by-nc/4.0
Fixed Point Theory in Graph-Structured Controlled Partial Metric Spaces with Applications to Integral Equations
In this paper, we introduce and investigate a new class of mappings called generalised graph \phi-contractions within the setting of Generalised Hausdorff Controlled Partial Metric (GHCPM) spaces. This framework integrates the structure of a graph with a controlled partial metric, providing a natural generalization of classical fixed point theories. Our study extends previous results by incorporating mappings defined on collections of non-empty closed and bounded subsets of a GHCPM space, and introducing contractive conditions governed by an upper semi-continuous and non-monotonic function. By leveraging the graph structure on GHCPM, we define a generalised graph contraction as a mapping that respects the connectivity induced by the graph while satisfying a contractive inequality involving the Hausdorff controlled partial metric. We establish novel fixed point theorems for such contractions, which unify and extend several existing results in the literature. To illustrate the applicability and generality of our results, we demonstrate the existence of solutions for nonlinear integral equations of Fredholm type. Concrete examples demonstrating the existence of fixed points under the proposed framework are also provided. These results open new directions in the study of fixed point theory in generalized metric spaces with additional structure.
Copyright (c) 2025 John Pamba, Hamilton Chirwa, Yolam Sakala, Alex Mungo https://creativecommons.org/licenses/by-nc/4.0
A Mathematical Model for the Saturation Effects of Radiotherapy with Oscillating Tumor Density
In the present-day society, cancer has become a challenge that threatens millions of human lives and causes many deaths. Throughout this research, we have developed a mathematical model to describe the radiotherapy treatment. There is a competition between tumor cells and normal cells; we use Lotka-Volterra dynamics to represent that biological idea in a mathematical model. In radiotherapy, ionizing particles attack the DNA of both tumor cells and normal cells. This process occurs in a medium with oxygenated tissues, and it has a saturation level. Previous researchers have not considered the saturation effects of radiotherapy in their models; however, our model incorporates the Michaelis-Menten term to represent these effects, which is the main novelty in this research with respect to previous works. We assume that other reactions are occurring according to the Mass Action Law, and also that radiotherapy targets both tumor cells and normal cells with the same intensity. First, we conduct a stability analysis of the system and then simulate the system by using time series analysis. We observed that in most cases, a stable equilibrium point can occur or periodic behavior may emerge in the population levels. By conducting a local sensitivity analysis, we identified the most sensitive parameters important in clinical treatments. We then conduct a bifurcation analysis for the most sensitive parameters, observing critical values for these parameters that must be maintained within a specific range to achieve an optimal treatment outcome. Primarily, we investigated the optimal range for the killing rate of tumor cells and discussed how the half-saturation constant effects therapy. These results will be crucial for achieving better clinical outcomes in radiotherapy.
Copyright (c) 2025 G.V.R.K. Vithanage, A.R.M. Hasini Parami Wattetenne, K.A. Nirupadhi Divyanjali Jayakody, M. Sawani Dhanushika, Sachith Dassanayaka https://creativecommons.org/licenses/by-nc/4.0
Convergence of θ-Milstein Method for Stochastic Differential Equations Driven by G-Brownian Motion
Although numerical methods for classical stochastic differential equations (SDEs) driven by Brownian motion are well-established, research on numerical schemes for SDEs driven by G-Brownian motion (referred to as G-SDEs) remains limited. Most existing studies are confined to Euler-Maruyama-type methods, which achieve only a strong convergence order of one-half. To bridge this gap, this paper aims to develop higher-order numerical methods for G-SDEs. By combining the classical Milstein method with the G-Itô formula, we propose a novel θ-Milstein scheme for G-SDEs. Using tools from G-expectation theory and Taylor expansions, we prove that the proposed scheme achieves a strong convergence order of one under the Lr-norm, assuming Lipschitz conditions. Numerical experiments demonstrate that the θ-Milstein method yields smaller errors and attains a higher convergence order compared to the Euler-Maruyama method, confirming its effectiveness and potential for advancing numerical solutions of G-SDEs.
Copyright (c) 2025 Shounian Deng, Bo Shen, Weiyin Fei https://creativecommons.org/licenses/by-nc/4.0
Abstract Dirichlet Problem for Elliptic System on Corner Domain
In this paper, we analyze abstract Dirichlet problem for elliptic system set on singular corner domain. We investigate the existence and uniqueness of strict solutions to the above problem using da Prato-Grisvard theory. The study is performed in the framework of little Hölder spaces.
Copyright (c) 2025 Belkacem Chaouchi, Marko Kostic, Daniel Velinov https://creativecommons.org/licenses/by-nc/4.0
Hopf Bifurcation of a Delay Commensalism System with Density Dependent Birth Rates
In ecology, commensalism and amensalism models are two kinds of important and interesting models. They have attracted much attention of ecologists and mathematicians in recent years. In this paper, we consider a two-species commensalism system with a discrete delay and density dependent birth rates. First, we investigate the characteristic equation of the proposed system and study the distribution of its roots. We obtain that, when the delay is sufficiently small, the positive equilibrium is locally asymptotically stable, when increases to a critical value, the positive equilibrium loses its stability and a Hopf bifurcation occurs, as continues to increase, a family of periodic solutions bifurcate from the positive equilibrium. Then, by using the normal form theory and the center manifold theorem, we derive the precise formulae to determine the Hopf bifurcation direction and the stability of the bifurcating periodic solutions. Numerical simulation results are included to support our theoretical analysis. We plot the trajectory graphs on , plane respectively. We also plot phase graphs to illustrate the change of stability of the positive equilibrium and arise of periodic solution. In order to fully validate the occurrence of Hopf bifurcation, we use the numerical continuation package DDE-Biftool to generate bifurcation diagrams and accurately track stability changes of the positive equilibrium and periodic solution with respect to the delay parameter . The commensalism model we propose considers both density dependent birth rate and time delay, it is of great practical and theoretical significance. The theoretical and numerical analysis that we do on the proposed system can make a supplement to the literature on the dynamics of delay commensalism systems. 2020 MSC: 34K18, 34K20, 92D25
Copyright (c) 2025 Tianyang Li, Qiru Wang https://creativecommons.org/licenses/by-nc/4.0
Vector Lattice Data Analysis: Fitting and Model Uncertainty
Functional data analysis (FDA) is a popular research area of data analysis that is well-suited for modeling complex data structures such as time series data and images. In Linear Regression models, the random variables are often described using a finite--dimensional vector space, under the assumption that the random variables are represented by a finite set of parameters. FDA allows us to model random variables as functions. This can lead to a more flexible and expressive approach to the statistical model. Within FDA, the specific paper investigates the potential of vector lattices to enhance model flexibility and address model uncertainty. The limitations of finite-dimensional vector spaces in capturing the complexities of real-world random variables are discussed. An investigation is conducted into the concept of Vector Lattice Linear Regression Models (VLLM), highlighting their ability to effectively handle model uncertainty.
Copyright (c) 2025 Christos Kountzakis, Amani Almohaimeed https://creativecommons.org/licenses/by-nc/4.0
Mathematical Modelling of the Health Impact of Air Pollution from Figuil Cement and Marble Works on the Respiratory System of the Local Population
Air pollution notably stemming from cement and marble industries has been identified as a significant factor contributing to deteriorating respiratory health in regions of high industrial density. Figuil region in northern Cameroon suffers a disturbing health impact from industrial facilities emitting fine particulate matter and sulphur dioxide heavily. Quantitatively assessing effect of pollutants on health of local populations remains primary objective of this somewhat obscure study mercifully. A mathematical model derived from SEIR model incorporates atmospheric pollutant concentrations as environmental forcing variables rather effectively nowadays. Innovation here integrates environmental epidemiological and demographic data dynamically into a spatio-temporal modelling framework enabling fairly accurate estimation of various exposure risks. Numerical simulations revealed a statistically significant correlation between peaks in PM₂.₅/SO₂ concentrations and increased cases of chronic bronchitis asthma and pneumonia during dry season. Regions near industrial sites show 2.8 times higher health risk compared with areas far away from such polluting facilities. Targeted public health interventions and industrial regulation are badly needed as underscored by these quite revealing data mercifully. Study proposes various mitigation measures including enhanced air quality monitoring around industrial sites and implementation of rather efficient filtration systems.
Copyright (c) 2025 Kikmo Wilba Christophe, Abanda Andre https://creativecommons.org/licenses/by-nc/4.0
Mathematical Modelling and Numerical Simulation of Hydrodynamics with Flood Mitigation Strategies in the Mayo-Danay Department of Cameroon's Far North Region
Flooding is the main structural problem faced by the Mayo-Danay department in the Far North Region of Cameroon, aggravated by climate change impacts, upstream deforestation, and the development and lack of maintenance of hydraulic infrastructure. This paper presents a new approach to develop a two-dimensional mathematical modelling combined with an advanced numerical simulation of hydrodynamics along the Logone River. The key originality aspect of this work lies in incorporating dynamic dyke breach scenarios together with seasonal real-time rainfall data allowing accurate flood propagation prediction at vital intervals. Flood risk mapping involves combining hydrodynamic behavior with topographic vulnerability parameters thus revealing areas under high risk. Detailed post-judgment analysis on Logone earthen dyke breach shows its highly destructive potential thereby emphasizing quite strongly the necessity for prevention strategies. Additionally, it evaluates sanitation infrastructure coupled with stormwater management through integrated urban drainage systems within this context. A preamble to what must be conceived as an exhaustive agenda for action is given by some recommendations: strengthening up Kousseri of the hydrometeorological network; satellite data and local observations complementing early warning systems; sustainable approaches that are reforested and integrated watershed managements done in parallelism with one another. The innovation lies in sophisticated digital and geospatial methodologies associated with territorial resilience strategies tailored to sub-Saharan contexts; this can be applied elsewhere where similar hydrological dynamics occur, thus providing a sound basis for scientific as well as political decision-making.
Copyright (c) 2025 Kikmo Wilba Christophe, Langola Olivier, Abanda Andre https://creativecommons.org/licenses/by-nc/4.0
Double Parametric Based Solution of Fuzzy Volterra Integral Equations with Separable Type Kernels
This paper presents a new approach for solving fuzzy Volterra integral equations with separable type kernels. Here triangular and trapezoidal fuzzy numbers are considered for the analysis. In general, the existing approaches first defuzzify the fuzzy integral equation into a crisp system of integral equations or two different crisp integral equations using the concept of fuzzy arithmetic. Then they solved them to obtain the lower and upper bounds of the fuzzy solution. However, using the proposed technique one has to solve only one crisp integral equation which is obtained by using the concept of double parametric form of fuzzy numbers. This makes the proposed approach more computationally efficient. Laplace Adomian Decomposition Method (LADM) has been implemented here to obtain the solution in double parametric form. The usefulness, and practicality of this method are demonstrated through various examples.
Copyright (c) 2025 Dennis Xavier, Diptiranjan Behera, Santhi Dennis Xavier https://creativecommons.org/licenses/by-nc/4.0
On Continuities via P-Statistical Convergence
This study investigates the concepts of P-statistical continuity (statistical continuity with respect to power series method) and P-statistical ward continuity (statistical ward continuity with respect to power series method) within the framework of power series methods, which extend the scope of statistical convergence beyond classical matrix methods. In the background, the limitations of traditional methods in capturing generalized continuity behaviors are explored and the use of power series as a versatile tool is motivated. Connections between these specialized forms of continuity and standard continuity are established, providing proofs and detailed properties. The results include several foundational theorems characterizing P-statistical continuity and ward continuity under various settings. These findings contribute to a more profound comprehension of continuity concepts within the context of regular summability methods. MSC: 26A15, 40A05, 40G10.
Copyright (c) 2024 Sevda Yıldız, Kamil Demirci https://creativecommons.org/licenses/by-nc/4.0
Fractional Inequalities for Exponentially s-Convex Functions on Time Scales
In this paper, we present new integral inequalities involving exponentially s-convex functions in the second sense on time scales. By utilizing the delta Riemann-Liouville fractional integral and the fractional Taylor formula, we establish upper bounds for functions that are n-times rd-continuously Δ-differentiable with exponentially s-convex properties. Our results provide novel insights into the theory of time scales, bridging the gap between discrete and continuous calculus. The application of fractional calculus on time scales is explored, and several well-known inequalities are employed to derive the main findings. These results have potential implications for further studies in fractional dynamic calculus and other related fields. AMS Subject Classification: 39A10, 39A11, 39A20.
Copyright (c) 2024 Svetlin G. Georgiev, Vahid Darvish https://creativecommons.org/licenses/by-nc/4.0
Forecasting Non-stationary Time Series Using Deep Learning in a Fuzzy Time Series Framework and its Application to Stock Markets
Non-stationary time series prediction is challenging due to its dynamic and complex nature. Fuzzy time series models offer a promising solution for forecasting such data, but a key challenge lies in partitioning the universe of discourse, which significantly impacts forecasting accuracy. Traditional fuzzy time series models often use equal-length interval partitioning, which is more suited for stationary data and limits their adaptability to non-stationary time series. This paper introduces a novel variable-length interval partitioning method designed specifically for non-stationary time series. The developed method combines a Long Short-Term Memory (LSTM) Autoencoder with K-means clustering, enabling dynamic, data-driven partitioning that adapts to the changing characteristics of the data. The LSTM Autoencoder encodes the time series, which is clustered using K-means, and intervals are defined based on cluster centers. Furthermore, the Variable Length Interval Partitioning-based Fuzzy Time Series model (VLIFTS) is developed by incorporating this partitioning method and the concepts of Markov chain and transition probability matrix. In this model, fuzzy sets are viewed as states of a Markov chain, and transition probabilities are used in the forecasting phase. The model is validated on stock market indices Nifty 50, NASDAQ, S&P 500, and Dow Jones. Stationarity and heteroscedasticity are tested using Augmented Dickey-Fuller (ADF) and Levene's tests respectively. Statistical forecast accuracy metrics Root Mean Squared Error (RMSE) and Mean Absolute Percent Error (MAPE) show that VLIFTS significantly improves forecasting accuracy over traditional models. This hybrid approach enhances fuzzy time series modelling and can be applied to various non-stationary time series forecasting problems.
Copyright (c) 2024 Abdul J. Saleena, John C. Jessy , M.C. Lineesh https://creativecommons.org/licenses/by-nc/4.0
A Study of an EOQ Model of Deteriorated Items with Pentagonal Dense Fuzzy Demand Rate
In this project work, we deal with an economic order quantity inventory model of deteriorating items under non-random uncertain demand. Here we consider the customers screen the fresh items during the selling period. After a certain period of time, the deteriorated items are sold at a discounted price. Firstly, we solve the crisp model, and then the model is converted into a fuzzy environment. Here we consider the pentagonal dense fuzzy, trapezoidal dense fuzzy, and triangular dense fuzzy for a comparative study. We have taken the numerical result using LINGO 18.0 software. Finally, sensitivity analysis and graphical illustration have been given to check the validity of the model.
Copyright (c) 2024 Aparna Maity, Jayeeta Hazra, Karuna K. Pal https://creativecommons.org/licenses/by-nc/4.0
Sign-changing Solutions for Fourth Order Elliptic Equation with Concave-convex Nonlinearities
In this paper, we study the following fourth order elliptic equation: Δ²u - Δu + V(x)u = κ(x)|u|q-2u + |u|p-2u in RN, where Δ² := Δ(Δ) is the biharmonic operator, 4 > N, 1 < q < 2 < p < 2* := 2N / (N - 4). Assuming that V(x) satisfies a class of coercive conditions and the nonnegative weighted function κ(x) belongs to Lp / (p-q)(RN), we obtain the existence of one sign-changing solution with the help of constraint variational method and quantitative deformation lemma. The novelty of this paper is that when the nonlinearity is the combination of concave and convex functions, we are able to obtain the existence of sign-changing solutions. Some recent results are improved and generalized significantly.
Copyright (c) 2024 Danni Zhang, Ziheng Zhang https://creativecommons.org/licenses/by-nc/4.0
Certain Fixed Point Results via Contraction Mappings in Neutrosophic Semi-Metric Spaces
In this work, the authors introduce the concept of neutrosophic semi-metric spaces and prove several common fixed-point theorems for countable and uncountable family of mappings via an implicit relation of contractive and integral type by utilizing locally integrable functions. These results improve and generalize the several results in the existing literature. Further, the authors present some non-trivial examples to support our main results. Mathematics Subject Classification: 46S40, 47H10, 54H25.
Copyright (c) 2024 Tayyab Kamran, Umar Ishtiaq, Khaleel Ahmad, Ghulam Murtaza, Ioannis Argyros https://creativecommons.org/licenses/by-nc/4.0
Enhancing Fruit Tree Yield Prediction with an Optimized Grey Neural Network Model Using the Fruit Fly Algorithm
This article first integrates data on fruit tree yield and related influencing factors in Fujian Province, covering two major categories of factors: social and natural. On this basis, this article calculated the correlation coefficients between fruit tree yield and various factors, verifying the rationality of indicator selection. Subsequently, this article used a combination of grey model GM (1,1), BP neural network model, and fruit fly algorithm to optimize the grey model and neural network for fruit tree yield prediction. In the end, based on the research results, it was found that the combination model of fruit fly algorithm optimized grey model and neural network has a better prediction effect on fruit tree yield, which is more suitable for us to deeply understand the changes in fruit tree yield. It can also be well trained for relatively random natural factors.
Copyright (c) 2024 Lingfeng Huang, Litao Guo https://creativecommons.org/licenses/by-nc/4.0
W2,p-Regularity of Lp Viscosity Solutions to Fully Nonlinear Elliptic Equations with Low-Order Terms
In this paper, we consider the following fully nonlinear elliptic equation F(D2u, Du, x) = f(x), where the operator F satisfies structure condition and the gradient of solution has Lploc growth rate particularly. We employ the technique from geometric tangential analysis whose basic principle is to transfer the good regularity of the recession operator to the original F by approximation methods and establish a prior local W2,p estimates for - Lp-viscosity solutions to the above equation. Mathematics Subject classification (2010): 35B45; 35R05; 35B65.
Copyright (c) 2024 Shuhan Hao, Yao Zhang, Zhenqiu Zhang https://creativecommons.org/licenses/by-nc/4.0
Biomagnetic Fluid Flow on a Nonlinearly Stretching Sheet with Variable Thickness in a Magnetic Environment
The main contribution of the current work is a numerical and mathematical investigation of the effects of magnetic dipole and electrical conductivity on the heat and flow transfer of biomagnetic fluid over a non-linear stretched sheet with variable thickness. Static magnetic fields are produced by magnetic dipoles, which are used in medical a pplications such as MRI, drug administration, and cancer therapy. Additionally, the impact of non-linear heat source/sink features was examined in the study, leading to an interesting phenomenon. The PDEs are attenuated to nonlinear ODEs with dealing appropriate similarity variables. These resultant ODEs are computed by developing an effective method emerged on the application of the finite differences technique. In the end, this section offers a summary of the implications resulting from different physical limitations on blood flow, including variable thickness and power index effects. It was discovered that the rise in Kelvin and Lorentz forces in the boundary layer significantly affected blood flow. The current findings for the biomagnetic fluid model are novel and inventive since they effectively expand upon the issues previously addressed by previously published scientific documentation.
Copyright (c) 2023 Md. Ghulam Murtaza, Jagadis C. Misra, Efstratios E. Tzirtzilakis, Mohammad Ferdows https://creativecommons.org/licenses/by-nc/4.0
Generalized Rational Type Contraction and Fixed Point Theorems in Partially Ordered Metric Spaces
In this article, we establish the existence and uniqueness of fixed points for rational type contraction mappings in a metric space that is equipped with a partial order. Our results are shown to improve upon previous results in the literature, and we provide illustrative examples to demonstrate the effectiveness of our approach. Mathematics Subject Classification: 47H10; 54H25.
Copyright (c) 2023 Muhammed Raji, Laxmi Rathour, Lakshmi N. Mishra, Vishnu N. Mishra https://creativecommons.org/licenses/by-nc/4.0
Solving System of Mixed Ordered Variational Inequalities Involving XOR and XNOR Operations in Ordered Product Banach Space
In this article, we study a generalized system of mixed ordered variational inequalities problems with various operations in a real ordered product Banach space and discuss the existence of the solution of our considered problem. Further, we discuss the convergence analysis of the proposed iterative algorithm using XNOR and XOR operations techniques. Most of the variational inequalities solved by the projection operator technique but we solved our considered problem without the projection technique. The results of this paper are more general and new than others in this direction. Finally, we give a numerical example to illustrate and show the convergence of the proposed algorithm in support of our main result has been formulated by using MATLAB programming. 2010 AMS Subject Classification: 47H09; 49J40.
Copyright (c) 2023 Iqbal Ahmad, Mohammad Farid, Syed S. Irfan https://creativecommons.org/licenses/by-nc/4.0
Analysis of Functional and Neutral Differential Equations via Lyapunov Functionals
We employ Lyapunov types functions and functionals and obtain sufficient conditions that guarantee the boundedness and the exponential decay of solutions, stability and exponential stability of the zero solution in nonlinear delay and neutral differential systems. The theory is illustrated with several examples. 2000 Mathematics Subject Classification: Primary 39A13, 39A23; Secondary 34K42
Copyright (c) 2023 Youssef N. Raffoul https://creativecommons.org/licenses/by-nc/4.0
A New Approach of Milne-type Inequalities Based on Proportional Caputo-Hybrid Operator
In this study, we first offer a novel integral identity using twice-differentiable convex mappings for the proportional Caputo-hybrid operator. Next, we demonstrate many integral inequalities related to the Milne-type integral inequalities for proportional Caputo-hybrid operator with the use of this newly discovered identity. Also, we present several examples along with their corresponding graphs in order to provide a better understanding of the newly obtained inequalities. Finally, we observe that the obtained results improve and generalize some of the previous results in the area of integral inequalities. 2010 Mathematics Subject Classification. 26D07, 26D10, 26A33
Copyright (c) 2023 İzzettin Demir https://creativecommons.org/licenses/by-nc/4.0
Generalized Legendre Polynomial Configuration Method for Solving Numerical Solutions of Fractional Pantograph Delay Differential Equations
This paper develops a numerical approach for solving fractional pantograph delay differential equations using generalized Legendre polynomials. These polynomials are derived from generalized Taylor bases, which facilitate the approximation of the underlying analytical solutions, leading to the formulation of numerical solutions. The fractional pantograph delay differential equation is then transformed into a finite set of nonlinear algebraic equations using collocation points. Following this step, Newton's iterative method is applied to the resultant set of nonlinear algebraic equations to compute their numerical solutions. An error analysis for this methodology is subsequently presented, accompanied by numerical examples demonstrating its accuracy and efficiency. Overall, this study contributes a more streamlined and productive tool for determining the numerical solution of fractional differential equations.
Copyright (c) 2023 Xueying Cui, Yuqiang Feng, Jun Jiang https://creativecommons.org/licenses/by-nc/4.0
Landslide Hazard Assessment Model for Slope Stability Analysis
Soil moisture dynamics is a complex phenomenon that depends on the atmospheric conditions, the geomorphological characteristics of the region under study, and the corresponding land use. It can be formally described by a diffusion model based on Darcy’s law and the law of mass continuity. In this work, the obtained numerical solution of the hydrological model has been exploited to evaluate the soil moisture in a given region and build a risk map for the slope stability of this region. More in detail, the infinite slope model from slope stability analysis has been used for evaluating the safety factor and constructing the corresponding quantitative hazard maps. Some results of the proposed method applied to a real case study are shown and discussed.
Copyright (c) 2023 Giulia De Santis, Nadaniela Egidi, Josephin Giacomini, Eleonora Gioia, Pierluigi Maponi, Lorenza Spadoni https://creativecommons.org/licenses/by-nc/4.0
Arithmetic Mean-Geometric Mean Inequality for Convex Fuzzy Sets
Convex analysis is a discipline of mathematics dedicated to the explication of the properties of convex sets and convex functions. Convex functions are extremely useful in proving many famous inequalities in mathematics. It is widely known that inequalities defined by convex functions originated with the works done by Holder and Jensen among others and applied to modeling a variety of problems both in hard and soft sciences. It is said that the arsenal of an analyst is heavily stocked with inequalities. Studies related to convexity have kept occupying a central position in almost all areas of mathematics, especially in functional analysis and operations research. Following the emergence of fuzzy set theory, fuzzy convexity alongside a number of related concepts has been explicated. However, not much has been done regarding fuzzy inequalities defined by fuzzy convexity. In this paper, a novel attempt to study arithmetic mean-geometric mean is proposed. In this short note, we provide two proofs of the arithmetic mean-geometric mean inequality for convex fuzzy sets. Mathematics Subject Classification 2020: 03E72, and 94D05.
Copyright (c) 2023 Dashrath Singh, Jai N. Singh https://creativecommons.org/licenses/by-nc/4.0