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# Differential Equations - Science topic

The study and application of differential equations in pure and applied mathematics, physics, meteorology, and engineering.
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Publications related to Differential Equations (10,000)
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In this article, a new integral transform called the AMJ transform method similar to Laplace transform, Sumudu transform, Elzaki transform and Aboodh transform is initiated. The advantage of this transform is that it solves the differential equation with nonvariable coefficient, three different examples are given and results are like minded.
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This study provides analytical approximate solutions to classes of nonlinear differential equations with generalized Caputo-type fractional derivatives. The Adomian decomposition method is successfully extended and modified to handle the considered fractional models. Our study displays the useful features of the modified scheme as an effective tech...
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This article investigates the impact of cognitive activities involved in teaching differential equations in secondary school. An analysis of textbooks is undertaken to identify the cognitive activities required from the students in learning and investing of differential equations. We noted the lack of support for the cognitive activities of changin...
Article
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This paper is concerned with the oscillation and asymptotic behavior of certain third-order nonlinear delay differential equations with distributed deviating arguments. By establishing sufficient conditions for the nonexistence of Kneser solutions and existing oscillation results for the studied equation, we obtain new criteria which ensure that ev...
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In this research paper, we procreate a framework to get ordinary differential equations (ODEs) involving fractional order derivatives using the techniques of Legendre wavelets. By the properties of Legendre wavelets, we analyze the application of second-order linear differential equations to the solution of algebraic equations. It demonstrates by t...
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Multi-dimensional uncertain differential equation is a tool to model an uncertain multi-dimensional dynamic system. Furthermore, stability has a significant role in the field of differential equations because it can be describe the effect of the initial value on the solution of the differential equation. Hence, the concept of almost sure stability...
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Evolutionary approaches are widely applied in solving various types of problems. The paper considers the application of EvolODE and EvolODES approaches to the identification of dynamic systems. EvolODE helps to obtain a model in the form of an ordinary differential equation without restrictions on the type of the equation. EvolODES searches for a m...
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In this manuscript a qualitative analysis to a nonlinear coupled system of pantograph impulsive fractional differential equations (PIFDEs) is established. By the use of Banach and Krasnoselskii’s fixed-point theorems some adequate conditions for the existence and uniqueness of solution to the considered problem are developed. The advantage of using...
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Our main purpose in this paper is to study the class of multi-term pantograph differential equations of fractional order. For the problem under consideration, some appropriate assumptions are provided for the establishment of existence of at least one solution. The existence as well as the uniqueness of solution to our problem is formulated using f...
Thesis
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The aim of this study is controlling of spurious oscillations developing around discontinuous solutions of both linear and non-linear wave equations or hyperbolic partial differential equations (PDEs). The equations include both first-order and second-order (wave) hyperbolic systems. In these systems even smooth initial conditions, or smoothly vary...
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We study hybrid fuzzy differential equations (HFDEs) under the Hukuhara derivative numerically using Picard’s and the general linear method (GLM). We use trapezoidal and triangular fuzzy numbers as the initial conditions. To demonstrate the efficiency of the proposed methods, the exact as well as the numerical solutions are presented numerically an...
Preprint
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The book is a collection of 28 articles (arXiv.org), which are devoted to the problem of strong (mean-square) approximation of iterated Ito and Stratonovich stochastic integrals in the context of numerical integration of Ito stochastic differential equations (SDEs) and non-commutative semilinear stochastic partial differential equations (SPDEs...
Article
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In this work, we are concerned with some qualitative analyses of fractional-order partial hyperbolic functional differential equations under the ψ-Caputo type. To be precise, we investigate the existence and uniqueness results based on the nonlinear alternative of the Leray-Schauder type and Banach contraction mapping. Moreover, we present two simi...
Article
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Cayley hash values are defined by paths of some oriented graphs (quivers) called Cayley graphs, whose vertices and arrows are given by elements of a group H. On the other hand, Brauer messages are obtained by concatenating words associated with multisets constituting some config- urations called Brauer configurations. These configurations define so...
Article
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This paper presents the comparison of the two Adams methods using extrapolation for the best method suitable for the approximation of the solutions. The two methods (Adams Moulton and Adams Bashforth) of step k = 3 to k = 4 are considered and their equations derived. The extrapolation points, order, error constant, stability regions were also deriv...
Article
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In this paper, we consider the following chemotaxis model with indirect signal consumption: ut=Δum−∇·(u∇v),x∈Ω,t>0,vt=Δv−vw,x∈Ω,t>0,wt=−δw+u,x∈Ω,t>0$$\left\{\begin{array}{ccc}\hfill {u}_t& =\Delta {u}^m-\nabla \cdotp \left(u\nabla v\right),\hfill & \hfill \kern2em x\in \Omega, t>0,\\ {}\hfill {v}_t& =\Delta v- vw,\hfill & \hfill \kern2em x\in \Ome... Article Full-text available 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 is a generalization of two important for applications types of nonlinearities: piecewise constant and... Article Full-text available In this paper, we study two types of second-order nonlinear differential equations with variable coefficients and mixed delays. Based on Krasnoselskii’s fixed point theorem, the existence results of positive periodic solution are established. It should be pointed out that the equations we studied are more general. Therefore, the results of this pap... Article Full-text available We study the existence of solutions of second-order nonlinear differential equations. It is shown that the second-order nonlinear differential equation x″=f(t,x,x′)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setleng... Article Full-text available In this paper, we present an approximation of the matching coverage on large bipartite graphs, for local online matching algorithms based on the sole knowledge of the remaining degree of the nodes of the graph at hand. This approximation is obtained by applying the Differential Equation Method to a measure-valued process representing an alternative... Article Full-text available This study addresses CuO-TiO2/CMC-water hybridnano-liquid in the influence of mixed convection flow and thermal radiative flow past a stretchable vertical surface. Cross nanofluid containing Titanium dioxide (TiO2), and Copper Oxide (CuO) are scattered in a base fluid of kind CMC water. In addition, theirreversibility analysis is also examined in t... Article Full-text available In this article, we derived conditions on the coefficient functions a(z) and b(z) of the differential equations y″(z)+a(z)y′(z)+b(z)y(z)=0 and z2y″(z)+a(z)zy′(z)+b(z)y(z)=0, such their solution f(z) with normalization f(0)=0=f′(0)−1 is starlike in the lemniscate domain, equivalently zf′(z)/f(z)≺1+z. We provide several examples with graphical presen... Article Full-text available Resumen La crisis por el COVID-19 que estamos enfrentando en este momento presenta retos importantes que vale la pena atacar. Consideramos que a partir del diseño e implementación de modelos confiables, podremos estudiar y analizar distintos escenarios, con la idea de dar predicciones y soluciones que pudieran serútiles para nuestro país. En este t... Article Full-text available Λ-fractional differential equations are discussed since they exhibit non-locality and accuracy. Fractional derivatives form fractional differential equations, considered as describing better various physical phenomena. Nevertheless, fractional derivatives fail to satisfy the prerequisites of differential topology for generating differentials. Hence... Article Full-text available Resumen: En este trabajo se desarrolla un Modelo Matemático (SIRR) , tipo SIR ,centrado en la tasa de infección, en la que se incluye la tasa de reprodución del virus, y la probabilidad de contaminación por acciones individuales, para simular los resultados de la enfermedad por el nuevo corona virus covid-19,(SRAS-COV-2, se muestra su aplicación es... Article Full-text available In this paper, linear quaternion differential equations (LQDEs) with delay attracts our attention. In the light of delayed quaternion matrix exponential and the method of variation of constants, we derive the solutions of homogeneous and nonhomogeneous LQDEs with delay under the assumption of permutation matrices. Further, we investigate the soluti... Article Full-text available In this work, we examine a class of nonlinear neutral differential equations. Krasnoselskii’s fixed-point theorem is used to provide sufficient conditions for the existence of positive periodic solutions to this type of problem. Article Full-text available This paper deals with the computational method for a class of second-order singularly perturbed parabolic differential equations with discontinuous coefficients involving large negative shift. The formulated method comprises the implicit Euler and the cubic-spline in compression methods for time and spatial dimensions, respectively. Intensive numer... Article Full-text available In this paper, we consider a class of third-order neutral impulsive differential equations. An equivalent class of neutral differential equations is obtained by using a suitable substitution. Some new oscillation results are proved. Moreover, we discuss the asymptotic behavior of the solution. The results in the abstract are illustrated via example... Article Full-text available In this paper, we study the neutrosophic differential equation by using the one-dimensional geometric AH-Isometry of Neutrosophic Laplace Transformation.Where we use this AH-isometry to find the algebraic image of this transformation, and then to apply this image directly on the problem of finding the solutions of differential equations. Article Full-text available The stability analysis of the numerical solutions of stochastic models has gained great interest, but there is not much research about the stability of stochastic pantograph differential equations. This paper deals with the almost sure exponential stability of numerical solutions for stochastic pantograph differential equations interspersed with th... Article Full-text available This manuscript aims to present the existence, uniqueness, and various kinds of Ulam’s stability for the solution of the implicit q-fractional differential equation corresponding to nonlocal Erdélyi-Kober q-fractional integral conditions. We use different fixed point theorems to obtain the existence and uniqueness of solution. For stability, we uti... Article Full-text available Computational simulation of natural phenomenon is currently attracting increasing interest in applied mathematics and computational physics. Mathematical software for simulation is limited by the availability, speed, and parallelism of high-performance computing. To improve the performance and efficiency of some numerical techniques, a step-by-step... Article Full-text available The nonlinear fractional differential equation (FDE) is discussed in this study. First, the research will investigate the existence and unique solution of the nonlinear differential equation to the Atangana-Baleanu fractional derivative in the sense of Caputo with the initial periodic condition, an integral boundary condition by Krasnoselskii's and... Poster Full-text available Int. J. of Dynamical Systems and Differential Equations - Article Review Acknowledgement - 31 August 2022 Article Full-text available In this article, a special expansion method is implemented in solving nonlinear integro-partial differential equations of 2 + 1 -dimensional using a special expansion method of G ′ / G , 1 / G . We obtained the solutions for 2 + 1 -dimensional nonlinear integro-differential equations in real physical phenomena. The method is applied on 2 + 1 -dimen... Article Full-text available This paper studies the existence of extremal solutions for a nonlinear boundary value problem of Bagley–Torvik differential equations involving the Caputo–Fabrizio-type fractional differential operator with a non-singular kernel. With the help of a new inequality with a Caputo–Fabrizio fractional differential operator, the main result is obtained b... Presentation Full-text available In this talk we establish an averaging principle on the real semi-axis for semi-linear equation $$\label{eqAb1} x'=\varepsilon (\mathcal A x+f(t)+F(t,x))$$ with unbounded closed linear operator \mathcal A and asymptotically almost periodic coefficients. Under some conditions we prove that there exists at least one asymp... Conference Paper Full-text available We establish an averaging principle on the real semi-axis for semi-linear equation x ′ = ε(Ax + f (t) + F (t, x)) (1) with unbounded closed linear operator A and asymptotically Poisson stable (in particular, asymptotically stationary, asymptotically periodic, asymptotically quasi-periodic, asymptotically almost periodic, asymptotically almost autom... Article Full-text available In this paper, we develop the Fourier transform approach to study the Hyers-Ulam stability of linear quaternion-valued differential equation with real coefficients and linear quaternion-valued even order differential equation with quaternion coefficients. It shows that Fourier transform is valid to find the approximate solutions for quaternion-valu... Article Full-text available In this paper, we investigate the existence and multiplicity of solutions for a class of quasi-linear problems involving fractional differential equations in the χ-fractional space Hκ(x)γ,β;χ(Δ). Using the Genus Theory, the Concentration-Compactness Principle, and the Mountain Pass Theorem, we show that under certain suitable assumptions the consid... Chapter Full-text available The notion of inclusion by generalized conformable differentiability is used to analyze fuzzy conformable differential equations (FCDE). This idea is based on expanding the class of conformable differentiable fuzzy mappings, and we use generalized lateral conformable derivatives to do so. We’ll see that both conformable derivatives are distinct and... Article Full-text available The main crux of this manuscript is to develop the theory of fractional hybrid differential equations with linear perturbations of second type involving ψ−Caputo fractional derivative of an arbitrary order α ∈ (0, 1). By applying Krasnoselskii fixed point theorem and some basic concepts on fractional analysis, we prove the existence of solutions fo... Article Full-text available The terminal value problem of differential equations has an important application background. In this paper, we are concerned with the terminal value problem of a first-order differential equation. Some sufficient conditions are given to obtain the existence and uniqueness results of solutions to the problem. Firstly, some comparison lemmas are est... Article Full-text available This survey paper is devoted to succinctly reviewing the recent progress in the field of oscillation theory for linear and nonlinear fractional differential equations. The paper provides a fundamental background for all interested researchers who would like to contribute to this topic. Article Full-text available The aim of this paper is to derive oscillation criteria of the following fourth-order differential equation with delay term r x z ′ ′ ′ x γ ′ + ∑ i = 1 n q i x f z η i x = 0 , under the assumption ∫ x 0 ∞ r − 1 / γ s d s = ∞ . The results are based on comparison with the oscillatory behaviour of second-order delay equations and the generalised Ricc... Article Full-text available This paper investigates the polynomial stability of neutral stochastic pantograph differential equations with Markovian switching (NSPDEsMS). Firstly, under the local Lipschitz condition and a more general nonlinear growth condition, the existence and uniqueness of the global solution to the addressed NSPDEsMS is considered. Secondly, by adopting t... Article Full-text available In this paper, a one-dimensional mathematical model for investigating the vibrations of structures consisting of elastic and weakly curved rods is proposed. The three-dimensional structure is replaced by a limit graph, on each arc of which a system of three differential equations is written out. The differential equations describe the longitudinal... Article Full-text available The authors study the oscillatory behaviors of solutions of higher-order nonlinear differential equations with a nonlinear neutral term. The right hand side of their equation contains both an advanced and a delay term, and either (or both) of them can be sublinear or superlinear. The influence of these terms on the oscillatory and asymptotic behavi... Preprint Full-text available In this paper, we develop a physics-informed neural network (PINN) model for parabolic problems with a sharply perturbed initial condition. As an example of a parabolic problem, we consider the advection-dispersion equation (ADE) with a point (Gaussian) source initial condition. In the d-dimensional ADE, perturbations in the initial condition dec... Article Full-text available This paper shows how to use the fractional Sumudu homotopy perturbation technique (SHP) with the Caputo fractional operator (CF) to solve time fractional linear and nonlinear partial differential equations. The Sumudu transform (ST) and the homotopy perturbation technique (HP) are combined in this approach. In the Caputo definition, the fractional... Article Full-text available This work aims to minimize a continuously differentiable convex function with Lipschitz continuous gradient under linear equality constraints. The proposed inertial algorithm results from the discretization of the second-order primal-dual dynamical system with asymptotically vanishing damping term addressed by Boţ and Nguyen (J. Differential Equati... Conference Paper Full-text available In this work we present an integrating factor approach for solving certain higher order differential equations (DE's) and a generalized method for solving Self-Adjoint Differential Equations. Article Full-text available In this article, the numerical solution of the mixed Volterra–Fredholm integro-differential equations of multi-fractional order less than or equal to one in the Caputo sense (V-FIFDEs) under the initial conditions is presented with powerful algorithms. The method is based upon the quadrature rule with the aid of finite difference approximation to C... Article Full-text available We demonstrate that a neural network pretrained on text and fine-tuned on code solves mathematics course problems, explains solutions, and generates questions at a human level. We automatically synthesize programs using few-shot learning and OpenAI’s Codex transformer and execute them to solve course problems at 81% automatic accuracy. We curate a... Article Full-text available English is the most widely used language in the world, and at the same time, English translation is becoming increasingly important. However, the traditional English translation model still has some problems, such as poor translation effect, repeated translation, translation solidification, and translation limitations caused by regional language di... Article Full-text available The paper considers a simple and well-known method for reducing the differentiability order of an ordinary differential equation, defining the first derivative as a function that will become the new variable. Practically, we attach to the initial equation a supplementary one, very similar to the flow equation from the dynamical systems. This is why... Preprint Full-text available Application of an Inquiry-Based Learning Space (ILS) GRAASP in the course of differential equations for engineering students within the framework of the project WP@ELAB Aplicación de un espacio de aprendizaje basado en Indagación (ILS) GRAASP en el curso de ecuaciones diferenciales para estudiantes de ingeniería en el marco del proyecto WP@ELAB Abs... Article Full-text available We consider the supercritical Hénon problem -Δu=C(α)|x|αupα-εinΩ,u>0inΩ,u=0on∂Ω,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} {\left\{ \begin{array}{l...
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Heart failure is one of the significant public health burdens in the world. According to WHO, 2 million people suffer heart failure worldwide. In this study, we propose a bivariate stochastic model for heart failure disease progression and recovery process, which helps to understand the underlying mechanisms of the recovery process and suggests str...
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ICMAS Conference Proceeding is the 3rd Edition of the College of Education, Mustansiriyah University Conferences. ICMAS involved Our Peer-Reviewed Papers that were reviewed and presented through the 3rd International Conference on Mathematics and Applied Sciences (ICMAS) held in the College of Education, Mustansiriyah University, Baghdad, Iraq, fro...
Article
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In this paper we study a system of two degenerate parabolic equations which defined in a bounded domain. Using concepts of parabolic for finding existence of the solutions of the Dirichlet control boundary problem and the existence of Periodic time-solutions were achieved with results presented in detail for the proposed system.
Article
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The variable fractional dimensions differential and integral operator overrides the phenomenon of the constant fractional order. This leads to exploring some new ideas in the proposed direction due to its varied applications in the recent era of science and engineering. The present papers deal with the replacement of the constant fractional order b...
Article
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We develop a randomized Newton’s method for solving differential equations, based on a fully connected neural network discretization. In particular, the randomized Newton’s method randomly chooses equations from the overdetermined nonlinear system resulting from the neural network discretization and solves the nonlinear system adaptively. We theore...
Article
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In this paper we define a novel neutrosophic differential equation by using neutrosophic thick function. In addition, we present the concept of Laplace transformation on neutrosophic thick function and apply this transformation to solve some neutrosophic differential equations. Also, we illustrate many examples to clarify the methods and algorithms...
Research
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In this section, initially, I mention that definition of the Laplace transform. After that, calculus of the images [1], Laplace Transforms of the Riemann-Liouville Fractional derivative, Caputo derivative, Grünwald-Letnikov and Miller-Ross Sequential Fractional derivatives [2] are mentioned in our thesis. Since, this definitions have many applicati...
Article
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Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects. Using the Laplace transform for solving differential equations, however, sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by analytical means. Thus, we need numerical inver...
Article
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This paper deals with a class of boundary value problems of second-order differential equations with impulses and discontinuity. The existence of single or multiple positive solutions to discontinuous differential equations with impulse effects is established by using the nonlinear alternative of Krasnoselskii’s fixed point theorem for discontinuou...
Article
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En este trabajo se propone un modelo matemático simple que representa la dinámica de juego juvenil para adolescentes de 11 a 18 años. Este modelo se encuentra definido por un sistema de 3 ecuaciones diferenciales; las cuales se fundamentan en procesos de tipo continuo. La especificación de las clases de nuestro modelo se basa en la clasificación gr...
Article
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In this paper we use "KUSHARE Transform" for solving the system of ordinary differential equations of first order and first degree.
Preprint
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Trajectory prediction has been widely pursued in many fields, and many model-based and model-free methods have been explored. The former include rule-based, geometric or optimization-based models, and the latter are mainly comprised of deep learning approaches. In this paper, we propose a new method combining both methodologies based on a new Neura...
Thesis
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In this thesis, we study the existence of solutions and controllability for retarded semilinear neutral differential equations with non-instantaneous impulses, non-local conditions, and infinite delay. First, we set the problem in a phase space satisfying the Hale-Kato axiomatic theory for retarded differential equations with infinite delay. Second...
Article
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An implicit time--fractal--fractional differential equation involving the Atangana's fractal--fractional derivative in the sense of Caputo with the Mittag--Leffler law type kernel is studied. Using the Banach fixed point theorem, the well-posedness of the solution is proved. We show that the solution exhibits an exponential growth bound, and, conse...
Preprint
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The aim of this paper is to give a sufficient and necessary condition of the generalized polynomial Liénard system with a global center (including linear typer and nilpotent type). Recently, Llibre and Valls [J. Differential Equations, 330 (2022), 66-80] gave a sufficient and necessary condition of the generalized polynomial Liénard system with a l...
Article
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In this paper, we study the full parabolic attraction–repulsion Keller–Segel model with a fractional diffusion in ℝn$${\mathbb{R}}^n$$ for n=2$$n=2$$ or 3. We are more interested in the question that whether the solutions exist globally or blow up in finite time, which was studied in the classical attraction‐repulsion Keller‐Segel model by Jin...