On almost periodic solutions of the differential equation x″(t)=Ax(t) in Hilbert spaces by Gaston M. N'Guerekata

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An Existence Result for Second-Order Impulsive Differential Equations with Nonlocal Conditions by Meili Li, Haiqiang Liu

“…The Leray-Schauder alternative is used to investigate the existence of solutions for second-order impulsive differential equations with nonlocal conditions in Banach spaces. …”
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Boundary Value Problems of Nonlinear Mixed-Type Fractional Differential Equations by Ping Yu, Hongju Li, Jian Ding, Yanli Ma

“…In this paper, by means of a fixed point theorem for monotone decreasing operators on a cone, we discuss the existence of positive solutions for boundary value problems of nonlinear fractional singular differential equation. The proof of the main result is based on Gatica–Oliker–Waltman fixed-point theorem. …”
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Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions by Adel Al-Rabtah, Shaher Momani, Mohamed A. Ramadan

“…Suitable spline functions of polynomial form are derived and used to solve linear and nonlinear fractional differential equations. The proposed method is applicable for 0<α≤1 and α≥1, where α denotes the order of the fractional derivative in the Caputo sense. …”
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Numerical method for solving the subdiffusion differential equation with nonlocal boundary conditions by Murat A. Sultanov, Vladimir E. Misilov, Makhmud A. Sadybekov

Subjects: “…differential equations…”
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Analytic Solutions of an Iterative Functional Differential Equations Near Regular Points by Lingxia Liu

“…The existence of analytic solutions of an iterative functional differential equation is studied when the given functions are all analytic and when the given functions have regular points. …”
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On Runge–Kutta-type methods for solving multidimensional stochastic differential equations by Jurgis Navikas

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New Iterative Method: An Application for Solving Fractional Physical Differential Equations by A. A. Hemeda

“…The new iterative method with a powerful algorithm is developed for the solution of linear and nonlinear ordinary and partial differential equations of fractional order as well. The analysis is accompanied by numerical examples where this method, in solving them, is used without linearization or small perturbation which con…firm the power, accuracy, and simplicity of the given method compared with some of the other methods.…”
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Terminal value problem for the system of fractional differential equations with additional restrictions by Oleksandr Boichuk, Viktor Feruk

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Burgers’ Equations in the Riemannian Geometry Associated with First-Order Differential Equations by Z. Ok Bayrakdar, T. Bayrakdar

“…We construct metric connection associated with a first-order differential equation by means of the generator set of a Pfaffian system on a submanifold of an appropriate first-order jet bundle. …”
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Existence and Uniqueness of Mild Solutions for Nonlinear Stochastic Impulsive Differential Equation by L. J. Shen, J. T. Sun

“…This paper investigates the existence and uniqueness of mild solutions to the general nonlinear stochastic impulsive differential equations. By using Schaefer's fixed theorem and stochastic analysis technique, we propose sufficient conditions on existence and uniqueness of solution for stochastic differential equations with impulses. …”
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Periodic Solutions Generated by Impulses for State-Dependent Impulsive Differential Equation by Qizhen Xiao, Binxiang Dai

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Convergence of numerical solution of stochastic differential equation for the self-thinning process by Petras Rupšys

“…In this paper from a practical viewpoint we apply a simple numerical method for solution of the stochastic differential equations by the Milstein's higher order method. …”
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Analysis of Two-Level Mesh Method for Partial Integro-Differential Equation by Quan Tang, Ziyang Luo, Xindong Zhang, Juan Liu

“…In this paper, we present two-level mesh scheme to solve partial integro-differential equation. The proposed method is based on a finite difference method. …”
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On the spectrum of weakly almost periodic solutions of certain abstract differential equations by Aribindi Satyanarayan Rao, L. S. Dube

“…In a sequentially weakly complete Banach space, if the dual operator of a linear operator A satisfies certain conditions, then the spectrum of any weakly almost periodic solution of the differential equation u′=Au+f is identical with the spectrum of f except at the origin, where f is a weakly almost periodic function.…”
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Devaney Chaos and Distributional Chaos in the Solution of Certain Partial Differential Equations by Xavier Barrachina, J. Alberto Conejero

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Dynamic Analysis of Nonlinear Impulsive Neutral Nonautonomous Differential Equations with Delays by Jinxian Li

“…A class of neural networks described by nonlinear impulsive neutral nonautonomous differential equations with delays is considered. By means of Lyapunov functionals and differential inequality technique, criteria on global exponential stability of this model are derived. …”
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Exploring the performance of ChatGPT for numerical solution of ordinary differential equations by Saso Koceski, Natasa Koceska, Limonka Koceva Lazarova, Marija Miteva, Biljana Zlatanovska

Subjects: “…artificial intelligence (ai), differential equations, numerical solution, chatgpt…”
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On ψ-Caputo Partial Hyperbolic Differential Equations with a Finite Delay by Mohammed S. Abdo, Mohammed Zakarya, Emad E. Mahmoud, Saeed M. Ali, Abdel-Haleem Abdel-Aty

“…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. …”
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Boundary value problems for partial differential equations with piecewise contant delay by Joseph Wiener

Subjects: “…partial differential equation…”
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