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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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Article
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This paper deals with some existence results for a class of conformable implicit fractional differential Hybrid equations with delay. The results are based on some suitable fixed point theorems. In the last section, we provide different examples to illustrate our obtained results.
Poster
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The subject of nonlinear analysis is of interest in its own right, and it also serves as a foundation for various fields of pure and applied mathematics. Researchers worldwide are actively analyzing and developing mathematical theories that can be applied to real-world problems. Through this conference, recent progress and advancements in different...
Poster
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A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Numerical and Computational Methods". Deadline for manuscript submissions: 31 July 2025
Article
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Resumo A modelagem de qualquer estrutura pode ocorrer por técnicas contínuas ou por métodos de discretização, ressalvando-se que as primeiras conduzem, em geral, a equacionamentos mais complexos e decorrentes sistemas de equações diferenciais. Acontece que o segundo tipo de análise é bastante recorrente e aplicado nos dias atuais, devido à acessibi...
Preprint
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Analytical solutions of differential equations offer exact insights into fundamental behaviors of physical processes. Their application, however, is limited as finding these solutions is difficult. To overcome this limitation, we combine two key insights. First, constructing an analytical solution requires a composition of foundational solution com...
Article
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Our aim in this work is to derive conditions and criteria for the oscillation of some differential equations of p-Laplace type with a delayed term. Therefore, we develop these criteria that confirm to us that the equations studied are oscillatory by applying comparison with lower-order equations and Riccati techniques . Finally, we can elucidate th...
Article
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In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac–Frenkel time-dependent variational principle. In recent years, it has attracted a lot of attention due to its wide appl...
Article
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The primary objective of this work is to establish new criteria to guarantee the oscillation of solutions for second-order differential equations with p-Laplace type operator. New prerequisites are presented in order to analyze the oscillatory features of the analyzed equation. To support these Öndings, we employed a range of analysis tools, creati...
Article
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In this study, a fourth-order nonlinear ordinary differential equation is considered. The specificity of nonlinearity lies in the presence of moving singular points, which hinders the application of classical theory that only works in the linear case. Two research problems are addressed in this work: the theorem of existence and uniqueness of the s...
Article
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In this paper, we investigate the oscillatory properties of fourth-order neutral delay differential equation solutions in the canonical situation. To our knowledge, this equation has received minimal research. We prove new improved features and relationships for the solution and the accompanying function. Based on these relationships, oscillation t...
Article
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This article introduces a new class of multi-variate Hermite-Frobenius-Genocchi polynomials and explores various characterizations of these polynomials. We examine their properties, including recurrence relations and shift operators. Using the factorization method, we derive differential, partial differential, and integrodifferential equations sati...
Article
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In this current study, first we establish the modified power Atangana-Baleanu fractional derivative operators (MPC) in both the Caputo and Riemann-Liouville (MPRL) senses. Using the convolution approach and Laplace transformation, the so-called modified power fractional Caputo and R-L derivative operators with non-singular kernels are introduced. W...
Article
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After several prior works in image encryption, where we utilized algebraic mathematical tools within matrix algebra to perform operations that scatter the color values of the image, transforming the image into an encrypted matrix that no longer represents the original image, we decided to explore the field of differential equations as a mathematica...
Article
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Se utiliza el efecto que causa la presencia de una masa puntual en las vibraciones de vigas para la detección de múltiples fisuras. Se presenta un método para detectar la presencia de varias fisuras en vigas vibrantes. Se utiliza un modelo de viga con masas puntuales y condiciones elásticas generales para desarrollar un método de detección de tres...
Article
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Objective: This study examines the obstacles students may encounter when learning to solve differential equations with mathematical problem-solving. Method: A qualitative study with observation and interviews was conducted on the 5th-semester students of the Mathematics Education Study Program, Khairun University, Ternate, who took the Differential...
Article
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A number of methods for solving differential equations are discussed in this article, along with the many fields of science and engineering that make use of them. To comprehend both naturally occurring and artificially created systems, one must be familiar with differential equations, which are mathematical models that depict the change of a quanti...
Article
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In this paper, the uniform eventual stability of nonlinear impulsive differential equations with fixed moments of impulse is examined using the vector Lyapunov functions which is generalized by a class of piecewise continuous functions. Together with comparison results, sufficient conditions for the uniform eventual stability are presented. Results...
Article
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El modelado y simulación de biorreactores son fundamentales para optimizar los procesos, mejorando la calidad y eficiencia de productos biotecnológicos. El objetivo de la investigación fue modelar y simular un biorreactor continuo de mezclado perfecto (CSTR) en Simulink de Matlab para procesos fermentativos, considerando variables clave como veloci...
Article
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Neste trabalho, apresentamos uma abordagem que combina métodos numéricos tradicionais de resolução de equações diferenciais com técnicas de machine learning, visando obter aproximações mais eficientes das soluções de equações diferenciais ordinárias (EDOs). Em particular, propomos a integração do método de Runge-Kutta para resolver problemas de val...
Article
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After several prior works in image encryption, where we utilized algebraic mathematical tools within matrix algebra to perform operations that scatter the color values of the image, transforming the image into an encrypted matrix that no longer represents the original image, we decided to explore the field of differential equations as a mathematica...
Conference Paper
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O estudo das Equações Diferenciais é um campo que aborda uma variedade de modelos físicos aplicados, dentre os quais o circuito elétrico RLC está inserido. Entre os diferentes tipos de equações diferenciais, estão as equações diferenciais ordinárias (EDOs), que envolvem apenas uma variável independente [1]. A solução de uma EDO resulta em uma famíl...
Article
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This study introduces a novel approach for investigating the solvability of boundary value problems for differential equations that incorporate both ordinary and fractional derivatives, specifically within the context of non-autonomous variable order. Unlike traditional methods in the literature, which often rely on generalized intervals and piecew...
Article
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Phytoplankton blooms exhibit varying patterns in timing and number of peaks within ecosystems. These differences in blooming patterns are partly explained by phytoplankton:nutrient interactions and external factors such as temperature, salinity and light availability. Understanding these interactions and drivers is essential for effective bloom man...
Article
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The aim of this paper is to build some new asymptotic and oscillatory results for nonlin-ear third-order unstable type advanced differential equations with noncanonical operators. Without assuming any extra conditions, the studied equation is transformed to a canoni-cal type equation and this reduced the number of classes of nonoscillatory solution...
Article
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In this note we unify the results of P. O. Frederickson and A. C. Lazer [J. Differential Equations 5 (1969), 26-270], A. C. Lazer [Electron. J. Differ. Equ. Conf., vol. 5, 2000, pp. 113–119], A. C. Lazer and D. E. Leach [Ann. Mat. Pura Appl. (4) 82 (1969), 49–68], J. M. Alonso and R. Ortega [Nonlinearity 9 (1996), no. 5, 1099–1111], and P. Korman a...
Preprint
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LaTeX is not a programming language, but can it still simulate differential equations? This work explores the surprising potential of raw LaTeX, powered by the PGF libraries, to handle numerical simulations of three types of differential equations: ordinary differential equations (ODEs), stochastic differential equations (SDEs), and partial differe...
Article
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This paper reviews modern approximate analytical methods for solving symmetric and non-symmetric dynamical problems, including the Perturbation Method using the Green function, the Regular Perturbation Method, the Adomian Decomposition Method, the Undetermined Coefficient Method, the Poincaré-Lindstedt Method, and Multiple-Scale Analysis. The appli...
Article
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Solving differential equations is an extensive topic in various fields, such as fluid mechanics and mathematical finance. The recent resurgence in deep neural networks has opened up a brand new track for numerically solving these equations, with the potential to better deal with nonlinear problems and overcome the curse of dimensionality. The Physi...
Article
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The objective of this paper is to demonstrate the existence and uniqueness (EU) of solutions to a class of Fractional Integro-Stochastic Differential Equations (FISDEs) by utilizing the fixed-point technique (FPT) and stochastic techniques. Additionally, the paper proves the continuous dependence (CD) of solutions on the initial data. We examine th...
Preprint
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Universal differential equations (UDEs) are an emerging approach in biomedical systems biology, integrating physiology-driven mathematical models with machine learning for data-driven model discovery in areas where knowledge of the underlying physiology is limited. However, current approaches to training UDEs do not directly accommodate heterogenei...
Article
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This research investigates the oscillation criteria of nonlinear second-order neutral differential equations with multiple delays, focusing on their noncanonical forms. By leveraging an innovative iterative technique, new relationships are established to enhance the monotonic properties of positive solutions. These advancements lead to the derivati...
Article
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The following article is a summary and application with results on the ZJ Transform to solve Differential, Partial, Integro Differential and Integral Equations, we use the Integral Transform to solve by a simpler algebraic way the reduction to simpler differential equations, the integral transform as such "maps" an equation in its original domain t...
Article
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This research focuses on studying the asymptotic and oscillatory behavior of a special class of even-order nonlinear neutral differential equations, including damping terms. The research aims to achieve qualitative progress in understanding the relationship between the solutions of these equations and their associated functions. Leveraging the symm...
Article
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In this paper, we prove some estimates of the distribution functions of the Kolmogorov diameters of solution's set to one class of the third‐order nonlinear differential equations with variable coefficients. The equation is defined on the entire real axis, and its coefficients are unbounded functions. Previously, such equations were studied in the...
Article
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In this paper, we demonstrate that neutral fractional evolution equations with finite delay possess a stable mild solution. Our model incorporates a mixed fractional derivative that combines the Riemann–Liouville and Caputo fractional derivatives with orders 0<α<1 and 1<β<2. We identify the infinitesimal generator of the cosine family and analyze t...
Preprint
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Differential equations are a crucial mathematical tool used in a wide range of applications. If the solution to an initial value problem (IVP) can be transformed into an oracle, it can be utilized in various fields such as search and optimization, achieving quadratic speedup with respect to the number of candidates compared to its classical counter...
Preprint
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Time-delayed differential equations (TDDEs) are widely used to model complex dynamic systems where future states depend on past states with a delay. However, inferring the underlying TDDEs from observed data remains a challenging problem due to the inherent nonlinearity, uncertainty, and noise in real-world systems. Conventional equation discovery...
Article
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In this paper, we present a computational method for solving the second‐order impulsive differential equations with loadings subject to integral boundary conditions based on the Dzhumabaev parametrization method. The idea of this method involves introducing additional parameters, reducing the original problem to solving a system of linear algebraic...
Article
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In this paper, we are concerned with the characterization of the blow-up and global solutions for free boundary parabolic equation with competing nonlocal nonlinearity and absorption where \(q, \alpha \ge 1\), \(p=0\) or \(p\ge 1\) and \(\gamma > 0\) are given constants. This study is motivated from the works [Abdelhedi and Zaag: J. Differential Eq...
Research
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Consider the fractional differential equation (FDE) of the form: D α y(t) = f (t) where D α is the Caputo fractional derivative of order α, 0 < α ≤ 1, and f (t) is a given function. This equation can describe systems with memory effects, such as viscoelastic materials or anomalous diffusion. 2. Wronskian for Fractional Solutions For fractional diff...
Research
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The integration of fractional variational calculus with Wronskian determinants offers a promising framework for analyzing complex differential equations, especially those involving fractional operators. This study introduces a novel methodology that utilizes Wronskian determinants to explore solution spaces and stability criteria in fractional vari...
Article
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El modelo Archard es un modelo lineal que describe el desgaste de un sistema deslizante. Sin embargo, si se desea aplicar este modelo a un sistema oscilante, se deben considerar algunas modificaciones y el uso de ecuaciones diferenciales puede ser una estrategia útil. En un sistema oscilante, las superficies de contacto realizan movimientos repetit...
Article
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En este trabajo se presenta un estudio teórico-experimental sobre la ley de enfriamiento de Newton, con temperatura variable. En el estudio teórico se resolvió una ecuación diferencial ordinaria lineal la cual permite calcular la temperatura de un objeto a lo largo de un periodo de tiempo. Para la sección experimental del estudio se realizaron dos...
Preprint
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In this article, we construct unique strong solutions to a class of stochastic Volterra differential equations driven by a singular drift vector field and a Wiener noise. Further, we examine the Sobolev differentiability of the strong solution with respect to its initial value.
Preprint
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This paper presents a novel deep learning-based approach named RealDiffFusionNet incorporating Neural Controlled Differential Equations (Neural CDE) - time series models that are robust in handling irregularly sampled data - and multi-head attention to align relevant multimodal context (image data, time invariant data, etc.) at each time point. Lon...
Article
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The fixed-point theorem is a fundamental result in mathematics that establishes the existence of a fixed point for certain types of functions. A fixed point of a function is a point in the domain of the function that maps to itself under the given function. The most well-known and widely used fixed-point theorem is the Banach fixed-point theorem. B...
Article
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The role of differential equations (DEs) in science and engineering is of paramount importance, as they provide the mathematical framework for a multitude of natural phenomena. Since quantum computers promise significant advantages over classical computers, quantum algorithms for the solution of DEs have received a lot of attention. Particularly in...
Article
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A new approach to the series expansion of iterated Stratonovich stochastic integrals with respect to components of a multidimensional Wiener process. The case of arbitrary complete orthonormal systems in Hilbert space. II Abstract. The article is Part IV of the author's work devoted to a new approach to the series expansion of iterated Stratonovich...
Article
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The generalized neutrosophic differential equation is a differential equation with neutrosophic real variable x + yI instead of classical real variable x. This research is devoted to studying the oscillation of generalized neutrosophic half linear second order differential equation with the negative and delayed neutral term as follows: ((+)´(+))´+...
Article
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The objective of this paper is to introduce the concept of Weak Fuzzy Complex differential equations. We have defined the general solution of the n-th order Weak Fuzzy Complex ordinary differential equation. That we have used a special isomorphism transformation function to write the WFC-ODE as two Real ODEs and solved them with respect to their ow...
Preprint
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This research employs Universal Differential Equations (UDEs) alongside differentiable physics to model viscoelastic fluids, merging conventional differential equations, neural networks and numerical methods to reconstruct missing terms in constitutive models. This study focuses on analyzing four viscoelastic models: Upper Convected Maxwell (UCM),...
Article
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The recently proposed complex number differential operator is used in formulating ordinary differential equations for the first time. The differential operator definition is totally different than the real number differentiation of complex valued functions. The basic definitions and properties of the differential operator are given first. Various l...
Article
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As equações diferenciais são uma importante ferramenta para solucionar problemas práticos, em que são construídos modelos matemáticos adequados para cada situação-problema. A modelagem farmacocinética permite estudar a distribuição e a concentração de remédios no organismo, esses modelos, além de serem utilizados para predição e cálculo da concentr...
Preprint
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Deep learning has proven to be a suitable alternative to least-squares (LSQ) fitting for parameter estimation in various quantitative MRI (QMRI) models. However, current deep learning implementations are not robust to changes in MR acquisition protocols. In practice, QMRI acquisition protocols differ substantially between different studies and clin...
Article
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We can recast the Riccati and Abel differential equationsinto new forms in terms of introduced integrating factors.Therefore, the Lie-type systems endowing with transformation Lie-groups$SL(2,{\mathbb R})$ can be obtained.The solution of second-order linearhomogeneous differential equation is an integrating factorof the corresponding Riccati differ...
Article
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This paper considers the stability of differential equation of Mackey-Glass type in the sense of Hyers and Ulam with initial condition. It also considers the Hyers-Ulam stability of Lasota equation with initial condition. Some illustrative examples are given.
Article
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In this paper, we obtain the formula of solution to the initial value problem for a hyperbolic partial differential equation with variable coefficient which is the modification of the famous D’ Alembert formula.
Article
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This paper introduces the integration of the Cobb-Douglas (CD) utility model with quantum computation using the Clairaut-type differential formula. We propose a novel economic-physical model employing envelope theory to establish a link with quantum entanglement, defining emergent probabilities in the optimal utility function for two goods within a...
Article
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RESUMO O Teorema da Existência e Unicidade de Equações Diferenciais Ordinárias (EDOs) pode ser considerado um dos pilares fundamentais da teoria das equações diferenciais, pois estabelece condições sob as quais uma EDO possui uma solução única e determinada em um intervalo específico. A importância desse teorema em diversos campos da matemática e d...
Experiment Findings
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The aim of this paper is to derive the oscillation criteria of fifth order neutral differential equation of the form By applying Riccati Transformation technique sufficient conditions for the oscillation of this equation is obtained.
Article
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A partir de 2007, se muestra en la literatura un enfoque teórico sobre la Modelación Matemática y una visión particular desde la Comunidad Internacional de Educación Matemática. Este artículo es un recuento de estudios empíricos realizados desde 2014 respecto a investigaciones e innovaciones educativas de un curso de Ecuaciones Diferenciales (ED),...
Article
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Thesis
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This thesis is a systematic study of semi-groups of bounded linear operators in the context of conformation derivation, in order to deal with an abstract (semilinear) Cauchy problem. We prove the existence and uniqueness of the mild solution to this problem by the fi�xed point theorem.
Article
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Periodic properties of solutions play an important role in characterizing the behavior of solutions of sufficiently complicated nonlinear differential equations. Sufficient conditions are established which ensure the existence of periodic (or almost periodic) solutions of certain second nonlinear differential equations. Using the basic tool Lyapuno...
Article
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The aim of this work is to study the existence of a periodic solutions of differential equations $\frac{d^{4} }{ dt^{4} }x(t) = Ax(t) + f(t)$. Our approach is based on the M-boundedness of linear operators, Fourier type, $B^{s}_{p, q}$-multipliers and Besov spaces.
Article
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In this article, we focus on investigating the optimal convergence order of error estimates for the stabilizer‐free weak Galerkin finite element method for a second‐order time‐dependent differential equation under low regularity assumptions. In most of the existing literature on stabilizer‐free weak Galerkin finite element methods, the exact soluti...
Article
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A new version of the mathematical theory of non-thin multilayer nonlinearly elastic Kauderer plates of symmetric structures has been constructed. The components of the stress-strain state (SSS) and boundary conditions on the side surface of the plate are considered functions of three spatial coordinates. The variant is based on the development of c...
Article
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The p-Laplacian fractional differential equations have been studied extensively because of their numerous applications in science and engineering. In this study, a class of p-Laplacian fractional differential equations with instantaneous and noninstantaneous impulses is considered. The existence and multiplicity results of solutions are obtained by...
Article
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Educational materials related to differential equations are included in the last chapter of mathematics in high school updated content of secondary education. Currently, the teaching methodology of the chapter "Differential Equations" is in a state of formation. The article examines the ways of using computer technology in teaching this chapter. Th...
Conference Paper
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Andrea Razmadze Mathematical Institute of Ivane Javakhishvili Tbilisi State University Tbilisi, Georgia Program Committee: I. Kiguradze (Chairman) (Georgia), R. P. Agarwal (USA), R. Hakl (Czech Republic), N. A. Izobov (Belarus), S. Kharibegashvili (Georgia), T. Kiguradze (USA), T. Kusano (Japan), A. Ponosov (Norway), M. Tvrdý (Czech Republic) Organ...
Article
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In this paper, we show the maximal regularity of nonlinear second-order hyperbolic boundary differential equations. We aim to show if the given second-order partial differential operator satisfies the specific ellipticity condition; additionally, if solutions of the function, which are related to the first-order time derivative, possess no poles no...
Article
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In this article, we studied the existence of solutions for a more general form of nonlinear fourth-order differential equations by using a new generalization of the Arzelá–Ascoli theorem and Schauder fixed theorem under easier and general conditions. Moreover, we provided some sufficient conditions on the nonlinear function that allowed us to deduc...
Article
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Traffic flow prediction is a critical task in intelligent transportation systems. However, cross-city data-driven prediction models encounter numerous challenges. A principal issue is data scarcity in underdeveloped cities, resulting from inadequate data collection mechanisms. Additionally, these models frequently rely exclusively on direct spatio-...
Article
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Este trabalho apresenta um estudo comparativo entre o princ´ıpio de extens˜ao de Zadeh e o princ´ıpio de extens˜ao sup - J0 na propagação de incerteza, focado em modelos populacionais descritos por equações diferenciais. Neste estudo, é considerado que as condições iniciais dos modelos são dados por intervalos, a fim de incorporar a incerteza intrí...
Article
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The research paper formulates a variable step block backward differentiation formula (VSBBDF) for solving nonlinear fuzzy differential equations (FDEs). Developed to address uncertainties within differential equations by using fuzzy environments, VSBBDF offers a flexible approach to solve equations with triangular fuzzy numbers. This method incorpo...
Article
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O presente artigo apresenta uma adaptação do modelo de corrida armamentista desenvolvido por Richardson, que é baseado em um sistema de equações diferenciais, via teoria dos conjuntos e lógica fuzzy. Para tanto implementamos um sistema de inferência fuzzy aliado com métodos numéricos tradicionais com o objetivo de solucionar as equações diferenciai...
Article
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In this paper, the authors obtain some new sufficient conditions for the oscillation of all solutions of Thomas–Fermi-type third-order nonlinear differential equations with advanced argument of the form (a2(t)(a1(t)y′(t))′)′−q(t)yα(σ(t))=0, under the assumptions that ∫t0∞1a2(t)dt<∞ and ∫t0∞1a1(t)dt=∞. The results are achieved by transforming the eq...
Conference Paper
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MÉTODOS RIGUROSOS PARA OBTENER LA DISTRIBUCIÓN DE CORRIENTE EN ANTENAS DE CONDUCTORES LINEALES Para calcular las distribuciones de corriente a lo largo de los elementos conductores de una antena es necesario obtener un modelo matemático de estos o sea de un sistema de ecuaciones integro-diferenciales a partir del empleo de expresiones generales par...
Article
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Durante a quarentena do Covid-19, muitas instituições de ensino adotaram o ensino remoto e implementaram metodologias como a modelagem matemática. Este estudo é uma pesquisa empírica sobre o uso de atividades de modelagem matemática com equações diferenciais no ensino remoto para alunos de engenharia, utilizando o Google Meet e o Moodle. A pesquisa...
Article
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This manuscript introduces a generalized operator and presents new Darbo-type fixed point theorems pivotal in the existence theory of integral and differential equations. The significance of these theorems lies in their ability to provide conditions under which solutions to complex mathematical problems can be guaranteed. We establish our results b...
Preprint
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Inspired by quantum mechanics, we introduce a weak form of solutions for differential equations and differential identities like Stokes theorem and Euler-Lagrange equation. We show that Schr\"{o}dinger equation is a weak from of the classical Euler-Lagrange equation.
Preprint
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This paper is concerned with a three-component chemotaxis model accounting for indirect signal production, reading as $u_t = \nabla\cdot(\nabla u - u\nabla v)$, $v_t = \Delta v - v + w$ and $0 = \Delta w - w + u$, posed on a smoothly bounded domain $\Omega\subset\mathbb R^n$, subject to homogeneous Neumann boundary conditions. It is suggested that...
Article
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Introdução: O biodiesel é um combustível renovável que contribui para uma matriz energética mais limpa. Sua produção pode ser otimizada por meio de estudos de simulação e modelagem. Objetivo: Simular a cinética da transesterificação de óleo vegetal com metanol, visando a conversão de triglicerídeos em ésteres metílicos. Métodos: Diferentes temperat...
Article
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The investment landscape in Nigeria is inherently influenced by economic fluctuations that pose substantial challenges and opportunities for investors and policyholders. This paper aims to investigate and provide solutions to the adverse effects of economic fluctuations on the investment returns of Insurance Industry in Nigeria through a numerical...