In this paper, we investigate finite-time stability analysis of fractional-order memristive fuzzy cellular neural networks(MFFCNNs) with time delay and leakage term. MFFCNNs are formulated by virtue of differential inclusion and set-valued map theories. By using generalized Bernoulli inequality and Holder inequality, we derived some new sufficient conditions of finite-time stability for the proposed

In this work, we use some results concerning the connection between blossoms and splines, especially those related to the smoothness conditions to develop an algorithm for constructing on an arbitrary triangulation a C2 spline approximant with minimal degree. Numerical tests are presented to illustrate the theoretical results.

Based on the diagonally compensated reduction, the preconditioned progressive iterative approximation (PPIA) for tensor product Bézier patches is presented. Due to the effectiveness of the preconditioner, the convergence rate of progressive iterative approximation (PIA) is accelerated significantly. To improve the robustness and reduce the computational complexity of PPIA, the inexact PPIA format for

A biofilm is a colony of microorganisms that adheres and grows on a surface typically in contact with a stagnant or flowing fluid environment. The hydrodynamic interaction between the fluid and the film structure plays a key role in the various phases of the biofilm life-cycle — formation, growth, detachment, and reestablishment. The fluid-flow conditions determine the shear stresses exerted upon the

In this study, we concentrate on the problem of a finite-time reliable filter design for discrete-time Takagi–Sugeno fuzzy semi-Markovian jump systems with time-varying delay, sensor faults and randomly occurring uncertainties. To be precise, the time-varying transition probability matrices for the considered system are described by a semi-Markov process. Specifically, the objective is to design a

For a static singular beam equation and a static non-uniform beam equation under external static loads, we develop boundary functions method (BFM) and energy boundary functions method (EBFM) to find the deflection curves, which automatically satisfy the boundary conditions. Furthermore, the EBFM is also designed to preserve the energy. Both methods can quickly find accurate numerical solutions of static

In this paper, two efficient two-grid algorithms with L1 scheme are presented for solving two-dimensional nonlinear time fractional diffusion equations. The classical L1 scheme is considered in the time direction, and the two-grid FE method is used to approximate spatial direction. To linearize the discrete equations, the Newton iteration approach and correction technique are applied. The two-grid

Recently, the concept of soft fuzzy rough covering was defined and their properties were studied by Zhan et al.. (Zhan and Sun, 2019). As a generalization of Zhan’s method (i.e., to increase the lower approximation and decrease the upper approximation), the present work aims to define the complementary fuzzy soft neighborhood and hence three new types of soft fuzzy rough covering models are constructed

In this paper, a class of two-level high order compact finite difference implicit schemes are proposed for solving the Burgers’ equations. Firstly, based on the fourth-order compact finite difference scheme for the spatial derivatives and the truncation error remainder correction method for the temporal derivative, the high-order compact (HOC) difference method is introduced for solving the one-di

This paper presents a modified graded mesh for singularly perturbed reaction–diffusion problems. The mesh we offer is generated recursively using Newton’s algorithm and some implicitly defined function. The problem is solved numerically using the finite element method based on polynomials of degree p≥1. We prove parameter uniform convergence of optimal order in ϵ-weighted energy norm. Test examples

In this paper, we construct numerical schemes based on the Lagrange polynomial interpolation to solve Fractional Sturm–Liouville problems (FSLPs) in which the fractional derivatives are considered in the Caputo sense. First, we convert the differential equation with boundary conditions into integral form and discretize the fractional integral to generate a system of algebraic equations in the matrix

The localized method of fundamental solutions is a recent domain-type meshless collocation method with the fundamental solutions of governing equations as the radial basis functions. This approach forms a sparse system matrix and has a higher efficiency than the traditional method of fundamental solutions. In this paper, a modified version of the localized method of fundamental solutions is developed

A common technique of enhancing thermal conducting is through the insertion of small magnetic particles or other nanoparticles with high thermal conductivity. In this research letter, manganese Zinc ferrite (MnZnFe2O4) and Nickle Zinc ferrite (NiZnFe2O4) were examined to assess the maximum possibility of enhancing thermal conductivity for current heat dissipation fluid problem. Therefore, a mathematical

The Nakagami distribution is widely applied in various areas such as communicational engineering, medical imaging, multimedia, among others. New MLE-like estimators in closed-form are proposed for the Nakagami parameters through the likelihood function of the generalized Nakagami distribution, which contains the Nakagami distribution as a special case. For the MLE-like estimators of the Nakagami distribution

We introduce a two sex age-structured mathematical model to describe the dynamics of HPV disease with childhood and catch up vaccines. We find the basic reproduction number (R0) for the model and show that the disease free equilibrium is locally asymptotically stable when R0≤1. We introduce an optimal control problem and prove that optimal vaccine solution exists and is unique. Using numerical simulation

Based on a new robust zeroing neural network (RZNN) model, the trajectory tracking control of a wheeled mobile robot (WMR) within fixed-time in noise-polluted environment is presented in this paper. Unlike most of the previous reported works, the RZNN model approach for trajectory tracking control of the WMR reaches fixed-time convergence and noise suppression simultaneously. Besides, detailed theoretical

We consider the systematic numerical approximation of Biot’s quasistatic model for the consolidation of a poroelastic medium. Various discretization schemes have been analysed for this problem and inf-sup stable finite elements have been found suitable to avoid spurios pressure oscillations in the initial phase of the evolution. In this paper, we first clarify the role of the inf-sup condition for

In this paper, we introduce the new Block Hybrid Third Derivative Nyström Method (BHTDNM) for the numerical solution of the one-dimensional Bratu’s problem via the boundary value approach. This method uses the derivative of the problem to generate better solutions. Also, we present the convergence analysis of the proposed method and demonstrate its advantages over various known methods through numerical

Drag and lift forces are very important in engineering applications and, therefore, many research projects have been conducted to control these forces. In this paper, the effects of an upstream porous plate on the hydrodynamic forces over a square cylinder are investigated using lattice Boltzmann method. The main idea is to separate the obstacle from the upstream flow by adding such a porous plate

This paper presents new synchronization results for a class of nonlinear discrete-time chaotic systems based on a synergetic observer design with a circuit implementation. The synchronization master–slave method adopted is based on the synergetic theory which is exploited to propose a synergetic observer. The system (master) adopted is that of the discrete-time Lur’e forms. One of the main contributions

In this work, we approximated a set of unknown physical parameters for a semi-empirical mathematical model of a PEMFC. We used an Estimation of Distribution Algorithm (EDA) known as UMDAG to find the tuple that best reproduces the experimental polarization curve. We tackled non-derivable objective functions to perform robust parameter estimation. We compared the sum of the squared error with published

In the paper, we aim to develop a class of high-order structure-preserving algorithms, which are built upon the idea of the newly introduced scalar auxiliary variable approach, for the multi-dimensional space fractional nonlinear Schrödinger equation. First, we reformulate the equation as an infinite-dimension canonical Hamiltonian system, and obtain an equivalent system with a modified energy conservation

This work presents a mathematical model describing the thin film formation during the co-evaporation of elements by PVD process for the production of CIGS type thin film photovoltaic cells. We propose a one-dimensional system of cross-diffusion Partial Differential Equations (PDEs) defined in a time-dependent space domain and introduce a numerical scheme for the discretization of the system. We calibrate

In this paper, we propose a new phase field model involving the p-Laplacian operator with 1

This paper presents the meshless method using radial polynomials with the combination of the multiple source collocation scheme for solving elliptic boundary value problems. In the proposed method, the basis function is based on the radial polynomials, which is different from the conventional radial basis functions that approximate the solution using the specific function such as the multiquadric function

We consider a coupled PDE–ODE model governing the bacterial dynamics of the anaerobic biodegradation of household waste in a landfill. The biological activity, represented with a non linear system of ordinary differential equations (ODE), takes place in an unsaturated porous medium represented by Darcy law. We transform the initial system of equations into a fully PDE model where the bacterial distribution

We study a steady state fluid–structure interaction problem between an incompressible viscous Newtonian fluid and an elastic structure using a nonlinear boundary condition of friction type on the fluid–structure interface. This condition, also known as Tresca slip boundary condition, allows the fluid to slip on the interface when the tangential component of the fluid shear stress attains a certain

In this work we deal with the regional observability problem, the purpose here is to reconstruct the initial state for a class of linear time-fractional systems, in a subregion ω of the evolution domain Ω, using an extension of Hilbert Uniqueness Method (HUM) introduced by Lions. This approach allows us to transform the regional reconstruction problem into a solvability one, which gives the initial

Product reviews are of great commercial value for online shopping market. The identification of customer opinions from product reviews is helpful to improve the marketing decisions of customers, sellers and producers. This paper proposes a novel framework for summarizing customer opinions from product reviews. Firstly, our framework identifies grammatically and semantically meaningful phrases which

In this paper, the conformable-time-fractional Klein–Fock–Gordon equation is considered and solved using the Kudryashov-expansion method to extract dual-wave solutions. Only, the quadratic and the cubic cases of the model are investigated. It has been noticed that physical changes in the construction of the obtained solutions are reported in the case of transition from the quadratic-state into the

In this research work, mathematical modeling for steady magnetized two-dimensional (2D) incompressible flow of Jeffrey nanofluid is developed over a stretched curved surface with combined characteristics of activation energy, Brownian motion, viscous dissipation, nonlinear mixed convection, magnetohydrodynamics (MHD), Joule heating and thermophoresis diffusion. Velocity slip condition is further imposed

The paper deals with the numerical realization of the 3D Stokes flow subject to threshold slip boundary conditions. The weak velocity-pressure formulation leads to an inequality type problem that is approximated by a mixed finite element method. The resulting algebraic system is non-smooth. Besides the pressure, three additional Lagrange multipliers are introduced: the discrete normal stress releasing

A model of groundwater flow in porous media influenced by wells (boreholes, channels) is considered. The model is motivated by the reduced dimension approach which suits fractured porous media problems, especially in granite rocks. The wells are modeled as lower dimensional 1d objects intersecting the surrounding bulk rock domain and causing singularities in the solution. The domains are discretized

This work investigates the functions of hardware-implemented intelligent decision support system using support vector machines. The system aims to forecast future productivity based on the data prepared by field experts followed by productivity influence factors. This feature is perceived by the combination of fuzzy logic and support vector machine. The proposed approach has been thoroughly tested

The whale optimization algorithm is based on the bubble-net attacking behavior of humpback whales and simulates encircling prey, bubble-net attacking and searching for prey to obtain the global optimal solution. However, the basic whale optimization algorithm has the disadvantage of search stagnation, easily falls into a local optimum, has slow convergence speed and has low calculation accuracy. The

Recurrent neural networks are designed to be convergent to the desired equilibrium point for their applications. Network parameter variations lead network states to other different points. So this paper discusses the prescribed convergence problem of recurrent neural networks with parameter variations. Firstly, we recurrent neural networks’ equilibrium point variation principles when parameters are

In this paper, an efficient method seeking the numerical solution of a time-fractional convection equation whose solution is not smooth at the starting time is presented. The Caputo time-fractional derivative of order in (0,1) is discretized by the L1 finite difference method using non-uniform meshes; and, for the spatial derivative the discontinuous Galerkin (DG) finite element method is used. The

In the present work, the model of diffuse pollution of the rivers by conservative components is considered on the basis of advection–diffusion equation. The asymptotic solutions of the equation are analyzed, and typical structures of stationary fields of pollutant concentration in the river are established. The model was tested using the measurements of pollutant concentrations on the reach of the

This article provides insight into the study of hydromagnetic flow of a chemically reacting water based nanofluid of Copper (Cu), Silver (Ag) and Ferrous Ferric Oxide (Fe3O4) nanoparticles over a stretching permeable sheet with heat generation, nanoparticle volume fraction, Soret number, Eckert number and porosity. The governing system of PDEs is reduced to nonlinear ODEs by the tool of similarity

The dynamic behavior of a fractional governor system is studied in this paper. The Stability and bifurcation of the equilibrium points of the system are investigated. We derive specific conditions for which the Hopf bifurcation of the fractional governor system may occur. It can be seen that different results are obtained compared to the classical mode. In the non-autonomous system, the tendency towards

This work investigates the finite-time event-triggered approach for recurrent neural networks with leakage term and its application. Here, decentralized event-triggered framework is recommended where event is checked at every sensor node related to local information for available triggering and the updated control is done whenever a centralized event is triggered. By handling the Lyapunov–Krasovskii

In rare event analysis, the estimation of the failure probability is a crucial objective. However, focusing only on the occurrence of the failure event may be insufficient to entirely characterize the reliability of the considered system. This paper provides a common estimation scheme of two complementary moment independent sensitivity measures, allowing to improve the understanding of the system’s

The purpose of the present article is to explore dynamical aspects of a stochastic childhood diseases model. For any initial value it is shown that the Markov process of proposed model is V-geometrically ergodic. Moreover, it is found that the solutions of the underlying model are stochastically ultimately bounded and permanent for any initial conditions. Some sufficient conditions are established

The purpose of this paper is to develop and analyze a mathematical model that represents the problem of unemployment in poor countries with limited availability of jobs. We are interested in studying the effect of training programs on the model’s dynamics. These training programs aim to improve the skills of unemployed people, contributing to a reduction of the unemployment rate. The model consists

In this article, we present optimal non-uniform finite difference grids for the Black–Scholes (BS) equation. The finite difference method is mainly used using a uniform mesh, and it takes considerable time to price several options under the BS equation. The higher the dimension is, the worse the problem becomes. In our proposed method, we obtain an optimal non-uniform grid from a uniform grid by repeatedly

In the present work, the rank upgrade method is suggested to obtain a periodic approximate solution for some complicated nonlinear problems. The method depends on obtaining an equivalent simple equation having a polynomial of nonlinearity without using the Taylor expansion. The solution process is extremely simple, as simple as that by the traditional perturbation method. This approach yields a highly

The quantity of information in images can be evaluated by means of the Shannon entropy. When dealing with natural images with a large scale of gray levels, as well as with images containing textures or suffering some degradation such as noise or blurring, this measure tends to saturate. That is, it reaches high values due to a large amount of irrelevant information, making it useless for measuring

Efficient detection of pests in different types of crops continues to be on today’s standards a difficult task. In order to address this problem, the implementation of an Integrated Pest Management (IPM) system involving the detection and classification of insects (pests) is essential for intensive production systems. Traditionally, this has been done by placing hunting traps and later manually counting

In this paper, the nonlinear dispersion wave model in both 1D and 2D is studied by the compact finite difference method, which is called the generalized Rosenau–RLW equation. A fourth-order compact three-level and linearized difference scheme that maintains the original conservative properties of equation is proposed. The discrete mass conservation and discrete energy conservation of compact difference

The axisymmetric longitudinal waves propagating in the long infinite cylindrical rod composed of material and structural constants, combinedly called as general incompressible materials, are derived using the perturbation reduction method as the far-field equation in the form of KdV equation in Dai and Huo (2002). In this work, the F expansion method is applied to the far-field equation and the properties

In this paper, we consider a fully discretization scheme for infinite age-structured population models with time-variable fertility rate and mortality rate. Based on the characteristics, the classical linear θ-methods with a kind of two-layer boundary condition are constructed for preserving an invariance of total populations. We are interested in the finite-time convergence and the stability for a

This paper is devoted to the study of numerical methods for solving large, sparse or full fractional linear algebraic systems (FLAS). The intent is to provide relevant and fair accuracy and efficiency comparisons of several solvers for this type of linear systems, typically involved in the approximation of fractional partial differential equations.

Vaccination programs for infants have significantly affected childhood morbidity and mortality. The primary goal of health administrators is to protect children against diseases that can be prevented by vaccination. In this manuscript, we have applied the homotopy perturbation Elzaki transform method to obtain the solutions of the epidemic model of childhood diseases involving time-fractional order

We present a tailored finite point method (TFPM) for anisotropic diffusion equations with a non-symmetric diffusion tensor on Cartesian grids. The fluxes on each edge are discretized by using a linear combination of the local basis functions, which come from the exact solution of the diffusion equation with constant coefficients on the local cell. In this way, the scheme is fully consistent and the

In this paper, a tumor-immune system with impulse comprehensive therapy and stochastic perturbation is investigated. The combination of pulsed chemotherapy and pulsed immunotherapy and the effect of environmental random disturbance are reflected in this model. The existence and uniqueness of global positive solution of the system are proved. It is determined that the expectation of the solution is

The stability and Hopf bifurcation have important effect on the design of neural networks. By revealing the effect of parameters on the stability and Hopf bifurcation of neural networks, we can better apply neural networks to serve humanity. This article is principally concerned with the stability and the emergence of Hopf bifurcation of fractional-order BAM neural networks with multiple delays. Applying

Considering the individual differences, spatial environment and the temporary acquired immunity, a general multi-group reaction–diffusion epidemic model with nonlinear incidence and temporary acquired immunity is proposed in this paper. The well-posedness of the solution including the existence of global solutions and the ultimate boundedness of the solutions are obtained, and then we define the basic

This numerical study exclusively focused on the direct two point diagonally multistep block method of order four (2DDM4) in the form of Adams-type formulas. The proposed predictor–corrector scheme was applied in this study to compute two equally spaced numerical solutions for the third-order two point and multipoint boundary value problems (BVPs) subject to Robin boundary conditions concurrently at

At present, the research on relevant decision-making considering the loss risk/ default risk in trade credit is on the rise This paper presents a supply chain model with a risk-averse retailer and a supplier offering loss sharing and trade credit in a supplier-Stackelberg game where the decision variables are the optimal order quantity and loss sharing ratio. The model is analyzed and compared to a

We derive conservation laws for so-called generalized nonlinear Schrödinger equation (GNLSE), which describes a propagation of super-short femtosecond pulse in a medium with cubic nonlinear response in the framework of slowly-evolving-wave approximation (SEWA). We take into account the beam diffraction, the pulse spreading due to second order dispersion, the pulse self-steepening, as well as mixed