Neutrosophic Semiopen Hypersoft Sets with an Application to MAGDM under the COVID-19 Scenario

Hypersoft set is a generalization of soft sets, which takes into account a multiargument function. The main objective of this work is to introduce fuzzy semiopen and closed hypersoft sets and study some of their characterizations and also to present neutrosophic semiopen and closed hypersoft sets, an extension of fuzzy hypersoft sets, along with few basic properties. We propose two algorithms based on neutrosophic hypersoft open sets and topology to obtain optimal decisions in MAGDM. The efficiency of the algorithms proposed is demonstrated by applying them to the current COVID-19 scenario

On New Solutions of Fuzzy Hybrid Differential Equations by Novel Approaches

The goal of this paper is to find the best of two sixth-order methods, namely, RK-Huta and RK–Butcher methods for solving the fuzzy hybrid systems. We state a necessary definition and theorem in terms of consistency for convergence, and finally, we compare the obtained numerical results of two different methods with analytical solution using two different numerical examples. In addition to that, we generalize the solutions obtained by RK-6 Huta and RK-6 Butcher methods (same order different stage methods) for both the problems we handled. We are proposing these two methods in order to reduce the error in accuracy and to establish these two methods are better than any other existing numerical methods. The best of two sixth-order methods are found by the error analysis study for both the problems. Also, we show whether the change in number of stages of same order methods affects the accuracy of the approximation or not

A Sampling Load Frequency Control Scheme for Power Systems with Time Delays

In this study, we investigate the effectiveness of a robust sampled-data H∞ load frequency control (LFC) scheme for power systems with randomly occurring time-varying delays. By using the input-delay technique, the sampled-data LFC model is reformulated as a continuous time-delay representation. Then, Bernoulli-distributed white noise sequences are used to describe randomly occurring time-varying delays in the sampled-data LFC model. Some less conservative conditions are achieved by utilizing the Lyapunov–Krasovskii functional (LKF) and employing Jensen inequality and reciprocal convex combination lemma to ensure the considered power system has mean-square asymptotic stability under the designed control scheme. The derived results are based on linear matrix inequalities (LMIs) that can readily be solved using the MATLAB LMI toolbox. The criteria obtained are used to analyze the upper bounds for time delays, and a comparison study to validate the efficacy of the presented method is presented

Global exponential stability of Clifford-valued neural networks with time-varying delays and impulsive effects

In this study, we investigate the global exponential stability of Clifford-valued neural network (NN) models with impulsive effects and time-varying delays. By taking impulsive effects into consideration, we firstly establish a Clifford-valued NN model with time-varying delays. The considered model encompasses real-valued, complex-valued, and quaternion-valued NNs as special cases. In order to avoid the issue of non-commutativity of the multiplication of Clifford numbers, we divide the original n-dimensional Clifford-valued model into $2^{m}n$ 2 m n -dimensional real-valued models. Then we adopt the Lyapunov&ndash;Krasovskii functional and linear matrix inequality techniques to formulate new sufficient conditions pertaining to the global exponential stability of the considered NN model. Through numerical simulation, we show the applicability of the results, along with the associated analysis and discussion.</jats:p

Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations

In this paper, we consider a class of singularly perturbed advanced-delay differential equations of convection-diffusion type. We use finite and hybrid difference schemes to solve the problem on piecewise Shishkin mesh. We have established almost first- and second-order convergence with respect to finite difference and hybrid difference methods. An error estimate is derived with the discrete norm. In the end, numerical examples are given to show the advantages of the proposed results (Mathematics Subject Classification: 65L11, 65L12, and 65L20)

Mixed ℋ-Infinity and Passive Synchronization of Markovian Jumping Neutral-Type Complex Dynamical Networks with Randomly Occurring Distributed Coupling Time-Varying Delays and Actuator Faults

This article examines mixed ℋ-infinity and passivity synchronization of Markovian jumping neutral-type complex dynamical network (MJNTCDN) models with randomly occurring coupling delays and actuator faults. The randomly occurring coupling delays are considered to design the complex dynamical networks in practice. These delays complied with certain Bernoulli distributed white noise sequences. The relevant data including limits of actuator faults, bounds of the nonlinear terms, and external disturbances are available for designing the controller structure. Novel Lyapunov–Krasovskii functional (LKF) is constructed to verify the stability of the error model and performance level. Jensen’s inequality and a new integral inequality are applied to derive the outcomes. Sufficient conditions for the synchronization error system (SES) are given in terms of linear matrix inequalities (LMIs), which can be analyzed easily by utilizing general numerical programming. Numerical illustrations are given to exhibit the usefulness of the obtained results

A study on fractional differential equations using the fractional Fourier transform

This study aims to use the fractional Fourier transform for analyzing various types of Hyers&ndash;Ulam stability pertaining to the linear fractional order differential equation with Atangana and Baleanu fractional derivative. Specifically, we establish the Hyers&ndash;Ulam&ndash;Rassias stability results and examine their existence and uniqueness for solving nonlinear problems. Simulation examples are presented to validate the results.</jats:p