99 Results Found

In this paper, we establish the existence of solutions to a nonlinear boundary value problem (BVP) of variable order at resonance. The main theorem in this study is proved with the help of generalized intervals and piecewise constant functions, in wh...

We find sufficient conditions for the unique solution of certain second-order boundary value problems to have a constant sign. To this purpose, we use the expression in terms of a Green’s function of the unique solution for impulsive linear per...

A numerical method is proposed for estimating piecewise-constant solutions for Fredholm integral equations of the first kind. Two functionals, namely the weighted total variation (WTV) functional and the simplified Modica-Mortola (MM) functional, are...

In this paper, the existence, uniqueness and stability of solutions to a boundary value problem of nonlinear FDEs of variable order are established. To do this, we first investigate some aspects of variable order operators of Hadamard type. Then, wit...

In this manuscript we introduce a quadratic integral equation of the Urysohn type of fractional variable order. The existence and uniqueness of solutions of the proposed fractional model are studied by transforming it into an integral equation of fra...

In this article, a nonlinear binary three-point non-interpolatory subdivision scheme is presented. It is based on a nonlinear perturbation of the three-point subdivision scheme: A new three point approximating $C^2$ subdivision scheme, where the converg...

Chlorinated solvents, common groundwater contaminants, can cause coexistence of the original contaminant and its degradation products during the transport process. Practically applicable analytical models for reactive transport are essential for simu...

The goal of this work is to study a multi-term boundary value problem (BVP) for fractional differential equations in the variable exponent Lebesgue space ($L^{p(·)}$). Both the existence, uniqueness, and the stability in the sense of Ulam–Hye...

Using variable-order fractional derivatives in differential equations is essential. It enables more precise modeling of complex phenomena with varying memory and long-range dependencies, improving our ability to describe real-world processes reliably...

In this paper, the existence of the solution and its stability to the fractional boundary value problem (FBVP) were investigated for an implicit nonlinear fractional differential equation (VOFDE) of variable order. All existence criteria of the solut...

IL-6 signaling plays an important role in inflammatory processes in the body. While a number of models for IL-6 signaling are available, the parameters associated with these models vary from case to case as they are non-trivial to determine. In this...

In this paper, we investigate differential equations with generalized piecewise constant delay, DEGPCD in short, and establish the existence and stability of a unique almost periodic solution that is exponentially stable. Our results are derived by u...

The semigroup properties of the Riemann–Liouville fractional integral have played a key role in dealing with the existence of solutions to differential equations of fractional order. Based on some results of some experts’, we know that th...

The hardware-accelerated time–frequency distribution calculation is one of the commonly used methods to analyze and present the information from intercepted radio frequency signals in modern ultra-wideband digital receiver (DRX) designs. In thi...

A new model of inertial neural networks with a generalized piecewise constant argument as well as unpredictable inputs is proposed. The model is inspired by unpredictable perturbations, which allow to study the distribution of chaotic signals in neur...

The stress-based finite element method is proposed to solve the static bending problem for the Euler–Bernoulli and Timoshenko models of an elastic beam. Two types of elements—with five and six degrees of freedom—are proposed. The el...

The exact solution of the movement equation of the Coriolis vibratory gyroscope (CVG) with a linear law of variation of the angular rate of rotation of the base is given. The solution is expressed in terms of the Weber functions (the parabolic cylind...

The authors investigate an epidemic model described by a differential equation, which includes a piecewise constant argument of the generalized type (DEPCAG). In this work, the main goal is to find an invariant region for the system and prove the exi...

An initial value problem for nonlinear fractional differential equations with a tempered Caputo fractional derivative of variable order with respect to another function is studied. The absence of semigroup properties of the considered variable order...

For the impulsive fractional-order system (IFrOS) of order $ϵ\in (1,2)$, there have appeared some conflicting equivalent integral equations in existing studies. However, we find two fractional-order properties of piecewise function and use them...

The phenomenon of coal cake collapse is often caused by the unstable operation of the elastic cam in a large coal cake tamper. Aiming at this problem, the mechanical characteristics of the composite rubber elements during cam rotation are studied. A...

This manuscript introduces a piecewise linear decomposition method devoted to a class of fractional-order dynamical systems composed of piecewise linear (PWL) functions. Inspired by the Adomian decomposition method, the proposed technique computes an...

In compressed sensing, it is believed that the L₀ norm minimization is the best way to enforce a sparse solution. However, the L₀ norm is difficult to implement in a gradient-based iterative image reconstruction algorithm. The total variation (TV) no...

This paper investigates a class of Hadamard variable-order fractional differential equations in which the fractional order is determined by the cumulative distribution function (CDF) of a continuous random variable. The proposed framework establishes...

Although fractional calculus has evolved significantly since its origin in the 1695 correspondence between Leibniz and L’Hôpital, the numerical treatment of multi-order fractional differential equations remains a challenge. Existing metho...

This paper presents direct and inverse theorems concerning the approximation of functions of several variables with bounded p-fluctuation using Walsh polynomials. These theorems provide estimates for the best approximation of such functions by polyno...

The highly oscillatory algebraic singular Volterra integral equations cannot be solved directly. A collocation numerical method is proposed to overcome the difficulty created by the highly oscillatory algebraic singular kernel. This paper is composed...

Computing an element of the Clarke subdifferential of a function represented by a program is an important problem in modern non-smooth optimization. Existing algorithms either are computationally inefficient in the sense that the computational cost d...

This paper is devoted to boundary-value problems for Riemann–Liouville-type fractional differential equations of variable order involving finite delays. The existence of solutions is first studied using a Darbo’s fixed-point theorem and t...

We construct a new volume preserving map from the unit ball ${\mathbb{B}}^3$ to the regular 3D octahedron, both centered at the origin, and its inverse. This map will help us to construct refinable grids of the 3D ball, consisting in diameter bounded cell...

This paper proposes new closed expressions of self-impedance using the Method of Moments with the Point Matching Procedure and piecewise constant and linear basis functions in different configurations, which allow saving computing time for the soluti...

The Cohen–Grossberg neural network is studied in the case when the dynamics of the neurons are modeled by generalized Caputo fractional derivatives with respect to another function (GCFDF). We consider a time-dependent delay and a switching rul...

This paper presents a novel and computationally efficient numerical method for solving systems of fractional-order differential equations using orthogonal hybrid functions (HFs). The proposed HFs are constructed by combining piecewise constant orthog...

We deal with two-dimensional copulas from the perspective of their differential entropy. We formulate a problem of finding a copula with maximum differential entropy when some copula values are given. As expected, the solution is a copula with a piec...

Motivated by the recent doubts concerning the compatibility of the purely imaginary one-dimensional cubic-oscillator model with the standard postulates of quantum mechanics, we propose to replace its potential $V\left(x\right)=i{x}^3$ by an elementary piece-wise con...

In this paper, we study nonlocal dynamics of a nonlinear delay differential equation. This equation with different types of nonlinearities appears in medical, physical, biological, and ecological applications. The type of nonlinearity in this paper i...

Intermittent tilting pouring is widely utilized in metal casting due to its operational simplicity and cost-effectiveness. However, this method faces challenges such as difficult manual tuning and inconsistency in achieving constant flow rates. Targe...

The comprehensive system of information security of an enterprise includes both tactical aspects of information and strategic priorities, reflecting the information policy and information strategy of the enterprise. Ensuring a given level of cybersec...

We study the asymptotic behavior in a neighborhood of zero of the sum of a sine series $g(\mathit{b},x)={\sum }_{k=1}^{\infty }{b}_{k}sinkx$ whose coefficients constitute a convex slowly varying sequence $\mathit{b}$. The main term of the asymptotics of the sum of such a series was obtained by...

The problem of obtaining a final expression for a function initially given in the form of a trigonometric Fourier series is considered. We consider a special case of a series when the coefficients of the series are known and are rational functions of...

We investigate a numerical method for approximating stochastic Caputo fractional differential equations driven by multiplicative noise. The nonlinear functions f and g are assumed to satisfy the global Lipschitz conditions as well as the linear growt...

Today, huge amounts of time series data are sensed continuously by AIoT devices, transmitted to edge nodes, and to data centers. It costs a lot of energy to transmit these data, store them, and process them. Data compression technologies are commonly...

This paper investigates the stability issues associated with neutral-type delay systems. Firstly, the delay-partitioning method is employed to construct a brand-new LK-functional candidate. The discrete delay and a neutral delay are divided into seve...

Fourier spectral methods for solving some linear stochastic space-fractional partial differential equations perturbed by space-time white noises in the one-dimensional case are introduced and analysed. The space-fractional derivative is defined by us...

We investigate the application of the Galerkin finite element method to approximate a stochastic semilinear space–time fractional wave equation. The equation is driven by integrated additive noise, and the time fractional order $\alpha \in (1,$...

This article introduces two numerical methods based on the Theory of Functional Connections (TFC) for solving linear ordinary differential equations that involve step discontinuities in the forcing term. The novelty of the first proposed approach lie...

Matrix differential equations with time delay are crucial to the modeling of complex multivariate systems. However, the existing semi-analytic Laplace residual power series method (LRPSM) literature mainly focuses on scalar or no-delay problems, and...

We study a finite-horizon optimal consumption and investment problem in a complete continuous-time market where consumption is restricted within fixed upper and lower bounds. Assuming constant relative risk aversion (CRRA) preferences, we employ the...

The asymptotic synchronization of quaternion-valued delayed neural networks with impulses and inertia is studied in this article. Firstly, a convergence result on piecewise differentiable functions is developed, which is a generalization of the Barba...

We consider a numerical approximation for stochastic fractional differential equations driven by integrated multiplicative noise. The fractional derivative is in the Caputo sense with the fractional order $\alpha \in (0,1)$, and the non-linear t...