Analytic Solutions for a Functional Differential Equation Related to a Traffic Flow Model by Houyu Zhao

“…We study the existence of analytic solutions of a functional differential equation (z(s)+α)2z'(s)=β(z(s+z(s))-z(s)) which comes from traffic flow model. …”
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Existence, uniqueness, and quasilinearization results for nonlinear differential equations arising in viscoelastic fluid flow by F. Talay Akyildiz, K. Vajravelu

“…Differential Equations and Nonlinear Mechanics…”
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Existence Theory for Pseudo-Symmetric Solution to 𝑝-Laplacian Differential Equations Involving Derivative by You-Hui Su, Weili Wu, Xingjie Yan

“…We all-sidedly consider a three-point boundary value problem for 𝑝-Laplacian differential equation with nonlinear term involving derivative. …”
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Two-Dimensional Fredholm Integro-Differential Equation with Singular Kernel and Its Numerical Solutions by Abeer M. Al-Bugami

“…In this paper, we introduce the nonlinear Fredholm integro-differential equation of the second kind with singular kernel in two-dimensional NT-DFIDE. …”
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Almost Surely Asymptotic Stability of Numerical Solutions for Neutral Stochastic Delay Differential Equations by Zhanhua Yu, Mingzhu Liu

“…We investigate the almost surely asymptotic stability of Euler-type methods for neutral stochastic delay differential equations (NSDDEs) using the discrete semimartingale convergence theorem. …”
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Existence and Monotone Iterative Approximation of Solutions for Neutral Differential Equations with Generalized Fractional Derivatives by Dussadee Somjaiwang, Parinya Sa Ngiamsunthorn

“…We study the existence and monotone iterative approximation of mild solutions of fractional-order neutral differential equations involving a generalized fractional derivative of order 0<α<1 which can be reduced to Riemann–Liouville or Hadamard fractional derivatives. …”
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Existence of Wave Front Solutions of an Integral Differential Equation in Nonlinear Nonlocal Neuronal Network by Lijun Zhang, Linghai Zhang, Jie Yuan, C. M. Khalique

“…The main idea we apply here is to reduce the nonlinear integral-differential equation into a solvable differential equation and test whether the solution we get is really a wave front solution of the model equation.…”
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Asymptotic Dichotomy in a Class of Fourth-Order Nonlinear Delay Differential Equations with Damping by Chengmin Hou, Sui Sun Cheng

“…All solutions of a fourth-order nonlinear delay differential equation are shown to converge to zero or to oscillate. …”
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Multiplicity Results to a Conformable Fractional Differential Equations Involving Integral Boundary Condition by Shuman Meng, Yujun Cui

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A delay-differential equation model of HIV related cancer--immune system dynamics by Urszula Foryś, Jan Poleszczuk

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Exact, approximate solutions and error bounds for coupled implicit systems of partial differential equations by Lucas Jódar

“…In this paper coupled implicit initial-boundary value systems of second order partial differential equations are considered. Given a finite domain and an admissible error ϵ an analytic approximate solution whose error is upper bounded by ϵ in the given domain is constructed in terms of the data.…”
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Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift by Gemechis File, Y. N. Reddy

“…International Journal of Differential Equations…”
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Physiology-informed regularisation enables training of universal differential equation systems for biological applications. by Max de Rooij, Balázs Erdős, Natal A W van Riel, Shauna D O'Donovan

“…The integration of neural networks and mechanistic models, forming universal differential equation (UDE) models, enables the automated learning of unknown model terms with less data than neural networks alone. …”
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Positive Solutions to Periodic Boundary Value Problems of Nonlinear Fractional Differential Equations at Resonance by Lei Hu

“…International Journal of Differential Equations…”
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Numerical Solution of Fractional Order Integro-Differential Equations via Müntz Orthogonal Functions by S. Akhlaghi, M. Tavassoli Kajani, M. Allame

“…In this paper, we derive a spectral collocation method for solving fractional-order integro-differential equations by using a kind of Müntz orthogonal functions that are defined on 0,1 and have simple and real roots in this interval. …”
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Positive Solutions for Systems of Nonlinear Higher Order Differential Equations with Integral Boundary Conditions by Yaohong Li, Xiaoyan Zhang

“…By constructing some general type conditions and using fixed point theorem of cone, this paper investigates the existence of at least one and at least two positive solutions for systems of nonlinear higher order differential equations with integral boundary conditions. …”
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Multivalued semilinear neutral functional differential equations with nonconvex-valued right-hand side by M. Benchohra, E. Gatsori, S. K. Ntouyas

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Convergence of Variational Iteration Method for Solving Singular Partial Differential Equations of Fractional Order by Asma Ali Elbeleze, Adem Kılıçman, Bachok M. Taib

“…We are concerned here with singular partial differential equations of fractional order (FSPDEs). The variational iteration method (VIM) is applied to obtain approximate solutions of this type of equations. …”
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Positive Solutions for a System of Hadamard-Type Fractional Differential Equations with Semipositone Nonlinearities by Youzheng Ding, Jiqiang Jiang, Donal O’Regan, Jiafa Xu

“…In this paper, we use the fixed-point index and nonnegative matrices to study the existence of positive solutions for a system of Hadamard-type fractional differential equations with semipositone nonlinearities.…”
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Fractional Variational Iteration Method for Solving Fractional Partial Differential Equations with Proportional Delay by Brajesh Kumar Singh, Pramod Kumar

“…International Journal of Differential Equations…”
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