Journal of Advances in Applied & Computational Mathematics
The Journal of Advances in Applied & Computational Mathematics is a peer-reviewed international journal dedicated to the publication of high-quality research in applied mathematics and computational mathematics. The journal provides a scholarly forum for the development, analysis, and application of mathematical methods addressing complex problems across science, engineering, technology, and interdisciplinary domains. Published by Avanti Publishers in academic affiliation with the Department of Mathematics at the University of Dayton, the journal is committed to maintaining rigorous peer review standards and strong editorial oversight.
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.
Existence, Uniqueness, and Ulam Stability of Conformable Integro-Dynamic Equations with Deviating Arguments on Time Scales
In this paper, we investigate a class of nonlinear conformable integro-dynamic equations with deviating arguments on time scales. By transforming the considered problem into an equivalent integral equation, sufficient conditions for the existence and uniqueness of solutions are established using Schauder’s and Banach’s fixed point theorems. Furthermore, Hyers–Ulam and generalized Hyers–Ulam stability results are derived under suitable assumptions. The obtained results extend several existing studies on nonlinear integro-dynamic equations within the framework of conformable calculus on time scales. AMS Subject Classifications: 34N05, 39A12, 34A08, 47H10.
Ulam–Hyers stability, Integro-dynamic equations, Conformable calculus on time scales, Nonlinear functional dynamic equations, Fixed point theory (Banach and Schauder).
Copyright (c) 2026 Mahammad Khuddush https://creativecommons.org/licenses/by-nc/4.0
Approximation Properties of Bivariate Extension of q-Stancu-Kantorovich Operators
In this paper we introduce a new q-Stancu-Kantorovich operators and we study some of their approximation properties. Furthermore, a Voronovskaja type theorem is also proven.
Copyright (c) 2015 Ana Maria Acu, Daniel Florin Sofonea https://creativecommons.org/licenses/by-nc/4.0
Detection and Discrimination of the Periodicity of Prime Numbers by Discrete Fourier Transform – Symphony of Primes
A novel representation of a quasi-periodic modified von Mangoldt function L(n) on prime numbers and its decomposition into Fourier series has been investigated. We focus on some particular quantities characterizing the modified von Mangoldt function. The results indicate that prime number progression can be decomposed into periodic sequences. The main approach is to decompose it into sin or cosine function. Basically, it is applied to extract hidden periodicities in seemingly quasi periodic prime function. Numerical evidences were provided to confirm the periodic distribution of primes.
Copyright (c) 2015 Journal of Advances in Applied & Computational Mathematics https://creativecommons.org/licenses/by-nc/4.0
The Methodological Aspect of Development and Application Multivariate Classification G-Mode for Analyses Geochemical Trend
This article is unique G-mode of multidimensional classification method and its application in the analysis of hydrogeochemistry Donetsk basin. He has the following main advantages over other methods of classification: does not require a priori information for classification of observations; earmarks homogeneous observing classes and subclasses; evaluates information weight of each indicator, determines the distance between the homogeneous taxon's; assessment of the descriptiveness of the sign of the classification and others. G-method is widely used to analyze geochemical, environmental, kosmochemical, distance and other types of information. The method successfully used in examining objects, phenomena and processes on Earth, Moon, Mars, Saturn, comets, asteroids and deep space. The results of the use of G-method in analysis of hydrogeological data for the Donetsk basin identified direct and inverse geochemical zonality. This shows that in the region can be discovered oil and gas accumulations.
Copyright (c) 2014 A.I. Gavrishin https://creativecommons.org/licenses/by-nc/4.0
Quantum Game Techniques Applied to Wireless Networks Communications
In order to analyze the power control problem, the wireless quantum network nodes are modeled as players at a quantum game. The power control problem is one of the most significant wireless communications challenges which characteristics make it proper to be modeled by means of game theory techniques. The problem results in non-cooperative game by nature, but, under quantum rules, a larger strategy space leads the players to choose a coalition strategy as the best option. Thus, the use of quantum game strategies makes possible the emergence of new equilibrium, which guarantees the best possible performance to the whole network. We show also that the whole network power consumption decreases when the intrinsic parallel behavior of quantum computation is capitalized. Moreover, the design of efficient medium access control algorithms is possible.
Uni-Type Modal Operators On Intuitionistic Fuzzy Sets
Intuitionistic Fuzzy Modal Operator was defined by Atanassov, he introduced the generalization of these modal operators. After this study, some authors defined some modal operators which are called one type and two type modal operator on intuitionistic fuzzy sets. In these studies, some extensions and characteristic properties were obtained. In this paper we defined new operators and examine some properties of them. In view of conclusions, it is shown that these operators are both one type and two type modal operators on Intuitionistic Fuzzy Sets. So, these common type modal operators are called uni-type modal operators on Intuitionistic Fuzzy Sets.
Numerical Hypercyclicity of Composition Operators on Classical Function Spaces: Power Boundedness, Fixed Points, and Linear Dynamics
This paper investigates numerical hypercyclicity for unweighted composition operators on several classical Banach and Hilbert spaces of functions. The aim is to compare this scalar orbit-density property with ordinary hypercyclicity and to determine when the two notions coincide. We consider composition operators on C([0,1]), H∞ (D), the disc algebra A(D), the Hardy space H2(D), the Bergman space A2(D), the Fock space F2(C), and the Dirichlet space D. The analysis combines power-boundedness arguments with known hypercyclicity criteria for composition operators. We show that power boundedness rules out both hypercyclicity and numerical hypercyclicity on C([0,1]), H∞ (D), A(D), and for bounded composition operators on F2(C). In contrast, for automorphism-induced composition operators on H2(D) and A2(D), numerical hypercyclicity is equivalent to ordinary hypercyclicity, and hence to the absence of fixed points of the symbol in D. For the Dirichlet space, we obtain partial results: elliptic automorphisms are shown not to induce numerically hypercyclic composition operators, while the remaining automorphic cases are reduced to an explicit scalar-orbit problem. The novelty of the paper lies in providing a unified and space-dependent comparison between numerical hypercyclicity and hypercyclicity for composition operators across these classical settings. 2020 Mathematics Subject Classification: 47A16, 47B33, 30H10, 47B38.
Composition operators, Numerical hypercyclicity, Power bounded operators, Hardy and Bergman spaces, Hypercyclicity and linear dynamics.
Copyright (c) 2026 Hadi O. Alshammari, Otmane Benchiheb, Marko Kostić https://creativecommons.org/licenses/by-nc/4.0
Novel Exact Traveling Wave Solutions of the (2+1)-Dimensional Calogero-Bogoyavlenskii-Schiff Equation via the Kumar-Malik and Improved F-Expansion Methods
This paper presents a rigorous investigation of analytical solutions for the (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (CBS) equation. To systematically analyze the nonlinear wave structures inherent in the CBS equation, we innovatively employ both the Kumar-Malik method and an improved F-expansion method, successfully constructing multiple families of exact solutions, including hyperbolic functions, trigonometric functions, and rational functions. Using the powerful mapping capabilities of Maple software, the obtained solutions are visualized as 3D plots, 2D graphs, and contour maps; through detailed analysis, kink wave solutions, singular periodic wave solutions, and rational singular solutions are clearly identified. These findings not only significantly expand the solution space for the integer-order CBS equation but also provide fresh theoretical insights into its dynamical characteristics. The results are expected to stimulate new research directions and facilitate substantial progress in nonlinear wave theory.
Kumar-Malik method, Traveling wave solutions, Nonlinear evolution equations, Improved F-expansion method, Calogero-Bogoyavlenskii-Schiff equation.
Copyright (c) 2026 Yiting Hu, Yuqiang Feng, Jun Jiang https://creativecommons.org/licenses/by-nc/4.0
Nonstandard Discretization Scheme in Volterra Integro-differential Equations that Preserves Uniform Asymptotic Stability
We apply a nonstandard discretization scheme to continuous Volterra integro-differential equations and we show that under this discretization, the necessary and sufficient conditions for uniform asymptotic stability of continuous Volterra integro-differential equations are preserved. Our analysis is based on the notion of resolvent. An example is provided as an application to our theory. 1991 Mathematics Subject Classification. Primary: 39A10, 34A97.
Copyright (c) 2026 Youssef N. Raffoul, Svetlin G. Georgiev, Halis C. Koyuncuoglu, Marko Kostic https://creativecommons.org/licenses/by-nc/4.0
Conditional Randomized Divergence Degree of Theories in the Fuzzy Propositional Logic System BL*
Using the concept of conditional probability and the randomization method of valuation sets, the conditional randomized truth degree of formulas is proposed in the fuzzy propositional logic system BL* with valuation domain [0,1]. The MP rule and HS rule for conditional randomized truth degrees are proven based on the semantics of BR0 algebra. At the same time, the concepts of conditional randomized similarity and conditional randomized pseudo-metric between formulas are introduced. It established a conditional randomized logic metric space. Within this conditional randomized logic metric space, the conditional randomized divergence of theories and its equivalent forms are proposed. Along with three different types of approximate reasoning modes, the relationships among them are discussed.
Fuzzy logic, Conditional randomized truth degree, Conditional randomized divergence degree, Conditional randomized logical metric space.
Copyright (c) 2026 Yin He, Xiaojing Hui, Chenxue Peng https://creativecommons.org/licenses/by-nc/4.0
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