9,250 Results Found

A linear autonomous differential equation with small delay is considered in this paper. It is shown that under a smallness condition the delay differential equation is asymptotically equivalent to a linear ordinary differential equation with constant...

We present a model that intermediates among the wave, heat, and transport equations. The approach considers the propagation of initial disturbances in a one-dimensional medium that can vibrate. The medium is nonlinear in such a form that nonlocal dif...

Nonsymmetric differential matrix Riccati equations arise in many problems related to science and engineering. This work is focusing on the sensitivity of the solution to perturbations in the matrix coefficients and the initial condition. Two approach...

In this paper, motivated by a biodegradable stent problem, we consider a parabolic differential equation on graphs. This kind of equation describes the stent material degradation in time. Since stents are mesh-like structures with thin struts, they c...

A new linear integro-differential equation is considered on a closed curve located on the complex plane. The integrals in the equation are understood in the sense of a finite part, according to Hadamard. The order of the equation can be higher than o...

In this paper, we extend the classical Lie symmetry analysis from partial differential equations to integro-differential equations with functional derivatives. We continue the work of Oberlack and Wacławczyk (2006, Arch. Mech. 58, 597), (2013, J. Mat...

This paper mainly consists of two parts: (i) We study the uniqueness, existence, and stability of a new fractional nonlinear partial integro-differential equation in ${\mathbb{R}}^n$ with three-point conditions and variable coefficients in a Banach space using inv...

In this paper numerical algorithms for solving fuzzy ordinary differential equations are considered. A scheme based on the 2nd Taylor method in detail is discussed and this is followed by a complete error analysis. The algorithm is illustrated by sol...

The Liu process is a fuzzy process whose membership function is a symmetric function on an expected value. The object of this paper was a fuzzy differential equation driven by Liu process. Since the existing fuzzy Euler solving methods (explicit Eule...

The purpose of the present paper is to study the presence of bifurcations of zero-Hopf type at a generalized Genesio differential equation. More precisely, by transforming such differential equation in a first-order differential system in the three-d...

Fractional Stochastic Differential Equations are becoming more popular in the literature as they can model phenomena in financial data that typical Stochastic Differential Equations models cannot. In the formulation considered here, the Hurst paramet...

A simple-form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback coefficien...

We consider first-order impulses for impulsive stochastic differential equations driven by fractional Brownian motion (fBm) with Hurst parameter $H\in ({\displaystyle \frac{1}{2}},1)$ involving a nonlinear $\varphi$-Laplacian operator. The system incorporates both state and der...

This paper is devoted to investigating the existence of solutions for the fractional differential equation and fractional differential inclusion of order $\alpha \in (2,3]$ with affine periodic boundary value conditions. Applying the Leray–Scha...

We derive a Hattendorff differential equation and a recursion governing the evolution of continuous and discrete time evolution respectively of the variance of the loss at time t random variable given that the state at time t is j, for a multistate M...

The sequential fractional differential equations at resonance are introduced subject to three-point boundary conditions. The emerged fractional derivative operators in these equations are based on the Caputo derivative of order that lies between 1 an...

For Euler’s differential equation of order n, a theorem is presented to give n solutions, by modifying a theorem given in a recent paper of the present authors in J. Adv. Math. Comput. Sci. 2018; 28(3): 1–15, and then the corresponding th...

A joint and unified vision of stochastic diffusion models associated with the family of hyperbolastic curves is presented. The motivation behind this approach stems from the fact that all hyperbolastic curves verify a linear differential equation of...

This paper focuses on the Caputo-Hadamard fractional uncertain differential equations (CH-FUDEs) governed by Liu processes, which combine the Caputo–Hadamard fractional derivative with uncertain differential equations to describe dynamic system...

The development of numeric-analytic solutions and the construction of fractional-order mathematical models for practical issues are of the greatest importance in a variety of applied mathematics, physics, and engineering problems. The Laplace residua...

Here, we center on the solvability of a fractional-order quadratic functional integro-differential equation with a nonlocal fractional-order integro-differential condition in the class of continuous functions. The maximal and minimal solutions will b...

In this paper, we present a qualitative study of an implicit fractional differential equation involving Riemann–Liouville fractional derivative with delay and its corresponding integral equation. Under some sufficient conditions, we establish t...

The Sturm–Liouville differential equation is an important tool for physics, applied mathematics, and other fields of engineering and science and has wide applications in quantum mechanics, classical mechanics, and wave phenomena. In this paper, we in...

In this paper, we are concerned with the combinations of the stochastic Itô-differential and the arbitrary (fractional) orders derivatives in a neutral differential equation with a stochastic, nonlinear, nonlocal integral condition. The existence of...

Many real-world problems have been modeled via delay differential equations. The pantograph delay differential equation $y^{\prime }\left(t\right)=ay\left(t\right)+by\left(ct\right)$ belongs to such a set of delay differential equations. To the authors’ knowledge, there are no standa...

The major goal of this manuscript is to investigate the existence, uniqueness, and stability of a q-fractional Langevin differential equation with q-fractional integral conditions. We demonstrate the existence and uniqueness of the solution to the pr...

In this article, we consider approximate solutions by quadratic splines for a fractional differential equation with two Caputo fractional derivatives, the orders of which satisfy $1<\alpha <2$ and $0<\beta <1$. Numerical computing schemes of...

In this study we treat TXO price as a dynamic system which changes over time and characterize it by differential equations. Our goal is to construct a model more suitable for TXO. We use ―Parabola Approximation‖ proposed by Li et al. (2011) to solv...

In this study, we consider and analyze an inhomogeneous Whittaker-type differential equation of the form ${\displaystyle \frac{d^{2}y\left(x\right)}{d{x}^2}}+{\displaystyle \frac{1}{x}}{\displaystyle \frac{dy\left(x\right)}{dx}}-{\alpha }^2\left(x^2-{\beta }^2\right)y\left(x\right)=g\left(x\right)$, where $\alpha$ and $\beta$ are given parameters. We investigate the analytical structu...

In this work, we study the asymptotic and oscillatory behavior of solutions to the second-order general neutral Emden–Fowler differential equation ${\left(a\left(v\right)\eta \left(x\left(v\right)\right)z^{\prime }\left(v\right)\right)}^{\prime }$ + $q\left(v\right)F\left(x\left(g\left(v\right)\right)\right)$ = 0, where $v\ge v_0$ and the corresponding function z = x + p$\left(x\right)$...

The existence of the advance parameter in a scalar differential equation prevents the application of the well-known standard methods used for solving classical ordinary differential equations. A simple procedure is introduced in this paper to remove...

In this paper, by using the characteristic system method, the kernel of a polynomial differential equation involving a derivation in ${\displaystyle R^n}$ is described by solving the Cauchy Problem for the corresponding first order system of PDEs. Moreover,...

In this manuscript, we explore how the solution of the matrix differential Riccati equation (MDRE) can be computed with the Extreme Theory of Functional Connections (X-TFC). X-TFC is a physics-informed neural network that uses functional interpolatio...

We propose a new non-convex fractional-order Weber multiplicative denoising variational generalized function, which leads to a new fractional-order differential equation, and prove the existence of a unique solution to this equation. Furthermore, the...

In this work, we present both analytical and numerical solutions to a seven-parameter confluent Heun-type differential equation. This second-order linear differential equation features three singularities: two regular singularities and one irregular...

In this paper, we studied the Hyers–Ulam–Rassias stability of Hermite’s differential equation, using Pachpatte’s inequality. We compared our results with those obtained by Blaga et al. Our estimation for $\left|z\left(x\right)-y\left(x\right)\right|$, where z i...

In this paper, we consider the Prabhakar fractional logistic differential equation. By using appropriate limit relations, we recover some other logistic differential equations, giving representations of each solution in terms of a formal power series...

The symmetry principle of circuit system shows that we can equate a complex structure in the circuit network to a simple circuit. Hence, this paper only considers a simple series RL circuit and first presents an uncertain RL circuit model based on mu...

The classical numerical methods for differential equations are a well-studied field. Nevertheless, these numerical methods are limited in their scope to certain classes of equations. Modern machine learning applications, such as equation discovery, m...

We use the representation of a continuous time Hattendorff differential equation and Matlab to compute ${}^2{\sigma }_t^{\left(j\right)}$, the solution of a backwards in time differential equation that describes the evolution of the variance of $L_t^{\left(j\right)}$, the loss at time t r...

We consider linear differential equations with variable delay of the form $$x^{\prime }\left(t\right)+p\left(t\right)x(t-\tau \left(t\right))=0,t\ge t_0,$$ where $p:[t_0,\infty )\to [0,\infty )$ and $\tau :$...

In this article, we investigate some qualitative properties of solutions to a class of functional differential equations with multi-delay. Using a modified approach, we first derive a number of optimized relations and inequalities that relate the sol...

This manuscript investigates a constrained problem of an arbitrary (fractional) order quadratic functional integro-differential equation with a quadratic functional integro-differential constraint. We demonstrate that there is at least one solution $x$...

This paper is concerned with the lattice Boltzmann (LB) method for a class of time fractional partial differential equations (FPDEs) in the Caputo sense. By utilizing the properties of the Caputo derivative and discretization in time, FPDEs can be ap...

Essential connections between the classical symmetry and nonclassical symmetry of a partial differential equations (PDEs) are established. Through these connections, the sufficient conditions for the nonclassical symmetry of PDEs can be derived direc...

In this paper, we first give some results on monic generalized Hermite polynomials (GHP) ${\{H_n^{(\mu )}(x)\}}_{n\ge 0}$, orthogonal with respect to the positive weight ${\left|x\right|}^{2\mu }{e}^{-x^2},\mu >-\frac{1}{2},x\in \mathbb{R}$, which will lead to the formulation of the seco...

The LLC resonant converter has been widely used in direct current (DC) power supply applications. However, fundamental harmonic approximation or other simplified analyses will introduce inevitable deviations. Therefore, the differential equation mode...

In this paper, we investigate functional inverse operators associated with a class of fractional integro-differential equations. We further explore the existence, uniqueness, and stability of solutions to a new integro-differential equation featuring...

In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions...

When studying the boundary value problems’ solvability for some partial differential equations encountered in applied mathematics, we frequently need to create systems of partial differential equations and explicitly construct linearly independ...