Search

In this paper, the sequential conformable Langevin-type differential equation is studied. A representation of a solution consisting of the newly defined conformable bivariate Mittag-Leffler function to its nonhomogeneous and linear version is obtained via the conformable Laplace transforms' technique. Also, existence and uniqueness of a global solution to its nonlinear version are obtained. The existence and uniqueness of solutions are shown with respect to the weighted norm defined in compliance with (conformable) exponential function. The concept of the Ulam–Hyers stability of solutions is debated based on the fixed-point approach. The LRC electrical circuits are presented as an application to the described system. Simulated and numerical instances are offered to instantiate our abstract findings. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the atomic solution of a special type of fractional partial differential equations. Tensor product in Banach spaces, some properties of atom operators, and some properties of conformable fractional derivatives are utilized in such process. JEL Classification: 34G10, 34A55 [ABSTRACT FROM AUTHOR]

In this paper, we develop the theoretical provisions of symmetric cryptographic algorithms based on the polynomial residue number system for the first time. The main feature of the proposed approach is that when reconstructing the polynomial based on the method of undetermined coefficients, multiplication is performed not on the found base numbers but on arbitrarily selected polynomials. The latter, together with pairwise coprime residues of the residue class system, serve as the keys of the cryptographic algorithm. Schemes and examples of the implementation of the developed polynomial symmetric encryption algorithm are presented. The analytical expressions of the cryptographic strength estimation are constructed, and their graphical dependence on the number of modules and polynomial powers is presented. Our studies show that the cryptanalysis of the proposed algorithm requires combinatorial complexity, which leads to an NP-complete problem. [ABSTRACT FROM AUTHOR]

Gumboro disease is a viral poultry disease that causes immune suppression on the infected birds leading to poor production, mortality, and exposure to secondary infections, hence a major threat in the poultry industry worldwide. A mathematical model of the transmission dynamics of Gumboro disease is developed in this paper having four compartments of chicken population and one compartment of Gumboro pathogen population. The basic reproduction number R og is derived, and the dynamical behaviors of both the disease-free equilibrium (DFE) and endemic equilibrium are analyzed using the ordinary differential equation theory. From the analysis, we found that the system exhibits an asymptotic stable DFE whenever R og < 1 and an asymptotic stable EE whenever R og > 1. The numerical simulation to verify the theoretical results was carried out using MATLAB ode45 solver, and the results were found to be consistent with the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we study asymptotic model change detection in multivariate linear regression by using the Kolmogorov–Smirnov function of the partial sum process of recursive residuals. We approximate the rejection region and also the power function of the test by establishing a functional central limit theorem for the sequence of the partial sum processes of the recursive residuals of the observations. When the assumed model is true, the limit process is given by the standard multivariate Brownian motion which does not depend on the regression functions. However, when the assumed model is not true (some models change), the limit process is represented by a vector of deterministic trend plus the standard multivariate Brownian motion. The finite sample size rejection region and the power of the test are investigated by means of Monte Carlo simulation. The simulation study shows evidence that the proposed test is consistent in the sense that it attains the power larger than the size of the test when the hypothesis is not true. We also demonstrate the application of the proposed test method to Indonesian economic growth data in which we test the adequacy of three-variate low-order polynomial model. The test result shows that the growth of the Indonesian economy is neither simultaneously constant nor linear. The test has successfully detect the appearance of a change in the model which is mainly caused by the COVID-19 pandemic in 2020. [ABSTRACT FROM AUTHOR]

Lymphatic filariasis is a leading cause of chronic and irreversible damage to human immunity. This paper presents deterministic and continuous-time Markov chain (CTMC) stochastic models regarding lymphatic filariasis dynamics. To account for randomness and uncertainties in dynamics, the CTMC model was formulated based on deterministic model possible events. A deterministic model's outputs suggest that disease extinction is feasible when the secondary threshold infection number is below one, while persistence becomes likely when the opposite holds true. Furthermore, the significant contribution of asymptomatic carriers was identified. Results indicate that persistence is more likely to occur when the infection results from asymptomatic, acutely infected, or infectious mosquitoes. Consequently, the CTMC stochastic model is essential in capturing variabilities, randomness, associated probabilities, and validity across different scales, whereas oversimplification and unpredictability of inherent may not be featured in a deterministic model. [ABSTRACT FROM AUTHOR]

This paper introduces a novel approach for solving first-order stiff initial value problems through the development of a one-step family of three optimized second-derivative hybrid block methods. The optimization process was integrated into the derivation of the methods to achieve maximal accuracy. Through a rigorous analysis, it was determined that the methods exhibit properties of consistency, zero-stability, convergence, and A-stability. The proposed methods were implemented using the waveform relaxation technique, and the computed results demonstrated the superiority of these schemes over certain existing methods investigated in the study. [ABSTRACT FROM AUTHOR]

This paper presents a study on the numerical solutions of the Burgers' equation with forcing effects. The article proposes three hybrid methods that combine two-point, three-point, and four-point discretization in time with the Galerkin finite element method in space (TDFEM2, TDFEM3, and TDFEM4). These methods use backward finite difference in time and the finite element method in space to solve the Burgers' equation. The resulting system of the nonlinear ordinary differential equations is then solved using MATLAB computer codes at each time step. To check the efficiency and accuracy, a comparison between the three methods is carried out by considering the three Burgers' problems. The accuracy of the methods is expressed in terms of the error norms. The combined methods are advantageous for small viscosity and can produce highly accurate solutions in a shorter time compared to existing numerical schemes in the literature. In contrast to many existing numerical schemes in the literature developed to solve Burgers' equation, the methods can exhibit the correct physical behavior for very small values of viscosity. It has been demonstrated that the TDFEM2, TDFEM3, and TDFEM4 can be competitive numerical methods for addressing Burgers-type parabolic partial differential equations arising in various fields of science and engineering. [ABSTRACT FROM AUTHOR]

This paper focuses on the impact of mosquito biting bias on the success of malaria intervention strategies. The initial model is developed considering the existence of symptomatic and asymptomatic humans, as well as vector bias. The model is then analyzed to demonstrate how the malaria-endemic equilibrium always exists and is globally asymptotically stable if the basic reproduction number is larger than one. On the other hand, malaria will always go extinct in the population if the basic reproduction number is less than one. For intervention analysis, the model is extended by considering mosquito repellent and hospitalization as control strategies. The control reproduction number is shown analytically. Using the Pontryagin maximum principle, we characterize our optimal control problem. Several scenarios are conducted to observe the dynamics of control variables under different circumstances. We found that the intervention of mosquito repellent and hospitalization together is the most cost-effective strategy to reduce the spread of malaria. Furthermore, we have shown that the more biased the vector attracted to infected individuals, the higher the cost needed to implement the control strategy. [ABSTRACT FROM AUTHOR]

The KdV-Burgers equation is one of the most important partial differential equations, established by Korteweg and de Vries to describe the behavior of nonlinear waves and many physical phenomena. In this paper, we reformulate this problem in the sense of Caputo fractional derivative, whose physical meanings, in this case, are very evident by describing the whole time domain of physical processing. The main aim of this work is to present the analytical approximate series for the nonlinear Caputo fractional KdV-Burgers equation by applying the Laplace residual power series method. The main tools of this method are the Laplace transform, Laurent series, and residual function. Moreover, four attractive and satisfying applications are given and solved to elucidate the mechanism of our proposed method. The analytical approximate series solution via this sweet technique shows excellent agreement with the solution obtained from other methods in simple and understandable steps. Finally, graphical and numerical comparison results at different values of α are provided with residual and relative errors to illustrate the behaviors of the approximate results and the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Cryptography has recently become a critical area to research and advance in order to transmit information safely and securely among various entities, especially when the transmitted data is classified as crucial or important. This is due to the increase in the use of the Internet and other novel communication technology. Many businesses now outsource sensitive data to a third party because of the rise of cloud computing and storage. Currently, the key problem is to encrypt the data such that it may be stored on an unreliable server without sacrificing the ability to use it effectively. In this paper, we propose a graph encryption scheme by using cryptography and steganography. Data is encrypted using association schemes over finite abelian groups and then hiding the encrypted data behind randomly chosen cover image. We implemented and evaluated the efficiency of our constructions experimentally. We provide experimental results, statistical analysis, error analysis, and key analysis that demonstrates the appropriateness and efficiency of the proposed technique. [ABSTRACT FROM AUTHOR]

In this paper, an efficient new technique is used for solving nonlinear fractional problems that satisfy specific criteria. This technique is referred to as the double conformable fractional Laplace-Elzaki decomposition method (DCFLEDM). This approach combines the double Laplace-Elzaki transform method with the Adomian decomposition method. The fundamental concepts and findings of the recently suggested transformation are presented. For the purpose of assessing the accuracy of our approach, we provide three examples and introduce the series solutions of these equations using DCLEDM. The results show that the proposed strategy is a very effective, reliable, and efficient approach for addressing nonlinear fractional problems using the conformable derivative. [ABSTRACT FROM AUTHOR]

Given that the Crimean and Congo hemorrhagic fever is one of the deadly viral diseases that occur seasonally due to the activity of the carrier "tick," studying and developing a mathematical model simulating this illness are crucial. Due to the delay in the disease's incubation time in the sick individual, the paper involved the development of a mathematical model modeling the transmission of the disease from the carrier to humans and its spread among them. The major objective is to comprehend the dynamics of illness transmission so that it may be controlled, as well as how time delay affects this. The discussion of every one of the solution's qualitative attributes is included. According to the established basic reproduction number, the stability analysis of the endemic equilibrium point and the disease-free equilibrium point is examined for the presence or absence of delay. Hopf bifurcation's triggering circumstance is identified. Using the center manifold theorem and the normal form, the direction and stability of the bifurcating Hopf bifurcation are explored. The next step is sensitivity analysis, which explains the set of control settings that have an impact on how the system behaves. Finally, to further comprehend the model's dynamical behavior and validate the discovered analytical conclusions, numerical simulation has been used. [ABSTRACT FROM AUTHOR]

This paper uses an augmented Lagrangian method based on an inexact exponential penalty function to solve constrained multiobjective optimization problems. Two algorithms have been proposed in this study. The first algorithm uses a projected gradient, while the second uses the steepest descent method. By these algorithms, we have been able to generate a set of nondominated points that approximate the Pareto optimal solutions of the initial problem. Some proofs of theoretical convergence are also proposed for two different criteria for the set of generated stationary Pareto points. In addition, we compared our method with the NSGA-II and augmented the Lagrangian cone method on some test problems from the literature. A numerical analysis of the obtained solutions indicates that our method is competitive with regard to the test problems used for the comparison. [ABSTRACT FROM AUTHOR]

The Pareto dominance-based evolutionary algorithms can effectively address multiobjective optimization problems (MOPs). However, when dealing with many-objective optimization problems with more than three objectives (MaOPs), the Pareto dominance relationships cannot effectively distinguish the nondominated solutions in high-dimensional spaces. With the increase of the number of objectives, the proportion of dominance-resistant solutions (DRSs) in the population rapidly increases, which leads to insufficient selection pressure. In this paper, to address the challenges on MaOPs, a knee point-driven many-objective evolutionary algorithm with adaptive switching mechanism (KPEA) is proposed. In KPEA, the knee points determined by an adaptive strategy are introduced for not only mating selection but also environmental selection, which increases the probability of generating excellent offspring. In addition, to remove dominance-resistant solutions (DRSs) in the population, an interquartile range method is adopted, which enhances the selection pressure. Moreover, a novel adaptive switching mechanism between angle-based selection and penalty for selecting solutions is proposed, which is aimed at achieving a balance between convergence and diversity. To validate the performance of KPEA, it is compared with five state-of-the-art many-objective evolutionary algorithms. All algorithms are evaluated on 20 benchmark problems, i.e., WFG1-9, MaF1, and MaF4-13 with 3, 5, 8, and 10 objectives. The experimental results demonstrate that KPEA outperforms the compared algorithms in terms of HV and IGD in most of the test instances. [ABSTRACT FROM AUTHOR]