D. Piriadarshani

This study investigates the use of the Laplace transform method to resolve a particular class of second-order linear initial-value neutral delay differential equations, which are prevalent in fields such as physics and engineering. By employing this analytical approach, we derive exact solutions that facilitate a deeper awareness of the dynamics of the system and its stability characteristics. A thorough illustrative example is provided to illustrate the Laplace transform method's efficacy, showcasing its practical utility in addressing real-world problems. This study not only highlights the advantages of the Laplace transform in providing clear insights into complex delay systems but also emphasizes its relevance in both theoretical and applied contexts.

In this paper the authors discuss a class of differential equations known as neutral delay differential equations (NDDEs) in which the delay occurs in the derivative with the highest order. They are encountered in various fields of applied sciences and are essential for mathematically representing real-world phenomena. It was challenging to discover approximate analytical solutions for certain methods. In this study, the researchers utilized the generalized Lambert W function to derive the characteristic roots for a first-order neutral delay differential equation featuring random delays. Numerical examples were then utilized to validate the obtained results.

In this paper the Bernoulli wavelets technique is applied to determine the numerical solution of singular ordinary differential equations. From a mathematical v In this paper the Bernoulli wavelets technique is applied to determine the numerical solution of singular ordinary differential equations. From a mathematical v

This study analyses PDA feedback, or delayed proportional derivative acceleration using a human balancing nonlinear model by applying Laplace Transform. The PDA This study analyses PDA feedback, or delayed proportional derivative acceleration using a human balancing nonlinear model by applying Laplace Transform. The PDA

The monkeypox virus causes a respiratory illness called monkeypox, which belongs to the Poxviridae virus family and the Orthopoxvirus genus. Although initially endemic in Africa, it has recently become a global threat with cases worldwide. Using the Antangana–Baleanu fractional order approach, this study aims to propose a new monkeypox transmission model that represents the interaction between the infected human and rodent populations. An iterative method and the fixed-point theorem are used to prove the existence and uniqueness of the symmetry model’s system of solutions. It shows that the symmetry model has equilibrium points when there are epidemics and no diseases. As well as the local asymptotic stability of the disease-free equilibrium point, conditions for the endemic equilibrium point’s existence have also been demonstrated. For this purpose, the existence of optimal control is first ensured. The aim of the proposed optimal control problem is to minimize both the treatment and prevention costs, and the number of infected individuals. Optimal conditions are acquired Pontryagin’s maximum principle is used. Then, the stability of the symmetry model is discussed at monkeypox-free and endemic equilibrium points with treatment strategies to control the spread of the disease. Numerical simulations clearly show how necessary and successful the proposed combined control strategy is in preventing the disease from becoming epidemic.

We consider an M / M / 2 queueing system subject to disasters and repair. Disasters occur only when there are active servers in the system. Whenever a disaster occurs, all customers in the system are washed out and the available servers in the system get failed. The failed servers are immediately taken to a repair facility and the repair starts immediately. Immediately after the repair, the server becomes active as new as it was before in the operable state and is now ready to render service to the available customers in the system. The repair facility is not affected by the occurrence of disasters. Customers are allowed to join the system at any time. For this model, we provide a transient analysis and deduce the steady-state distribution of the system size. We also provide some performance measures of the system. A numerical illustration is also provided to highlight the system behaviour.

The exact expectation of the financial backers with respect to the securities exchanges helps them in taking better independent directions. The financial backers utilize the measurable information accessible in the online media regarding stocks and shares, to help the investors in better planning and preparation. Metrics are an integral part of Linear Regression Model Assessment. This paper concentrates on the assessment of metrics in direct relapse contrasting the two financial exchanges in particular IBM and DELL stocks whose probabilities of building forecast of protection market costs abuse utilizing chronicled information.

The significant objective of this work is to utilize a fuzzy model called Fuzzy Linguistic Cognitive Maps to investigate a real-world problem. Fuzzy Linguistic Cognitive Maps is a fuzzy model that works on the notion of Fuzzy Cognitive Maps. The inclusion of linguistic variables in Fuzzy Cognitive Maps has added the advantage of obtaining the result in a more refined way. Uncertainty prevails all over the world. The human relationship and their behavior is the perfect example of vagueness. Their thoughts, actions and behavior keep on changing depending on the previous experience. The one to one relation between the domestic workers and the owners is highly uncertain. In this paper, the factors that are majorly affected by the domestic workers in their occupation are discussed. Also, the intensity of the attributes contributing to the problem is obtained in an optimized manner.

In this paper, different types of electrical circuits were modelled and their stochastic sources were computed for different kinds of sources using Caputo Fabri