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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Oscillation Criteria for Linear Neutral Delay Differential Equations of First Order by Fatima N. Ahmed, Rokiah Rozita Ahmad, Ummul Khair Salma Din, Mohd Salmi Md Noorani

“…Some new sufficient conditions for oscillation of all solutions of the first-order linear neutral delay differential equations are obtained. Our new results improve many well-known results in the literature. …”
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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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Applications of the neuro-evolutionary approach to the parabolic type partial differential equations by Waseem, Asad Ullah, Emad A.A. Ismail, Fuad A. Awwad

“…This work aims to investigate the Cuckoo search-active set algorithm (CS-ASA), which is based on the artificial neural network (ANN) approach to the nonlinear partial differential equations (PDEs). CS-ASA technique modifies the Cuckoo search best possible solution to the next stage. …”
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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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Applications of Schauder’s Fixed Point Theorem to Semipositone Singular Differential Equations by Zhongwei Cao, Chengjun Yuan, Xiuling Li

“…We study the existence of positive periodic solutions of second-order singular differential equations. The proof relies on Schauder’s fixed point theorem. …”
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The Extended Trial Equation Method for Some Time Fractional Differential Equations by Yusuf Pandir, Yusuf Gurefe, Emine Misirli

“…Nonlinear fractional partial differential equations have been solved with the help of the extended trial equation method. …”
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Some Existence Results for a System of Nonlinear Fractional Differential Equations by Eskandar Ameer, Hassen Aydi, Hüseyin Işık, Muhammad Nazam, Vahid Parvaneh, Muhammad Arshad

“…This paper presents some common fixed point theorems and an application to resolve a system of nonlinear fractional differential equations. Some examples and consequences are also given.…”
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A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations by Özkan Güner, Adem C. Cevikel

“…We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. …”
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Existence of Periodic Solutions for Nonlinear Fully Third-Order Differential Equations by Yunfei Zhang, Minghe Pei

“…In this paper, we study the existence of periodic solutions to nonlinear fully third-order differential equation x‴+ft,x,x′,x″=0,t∈ℝ≔−∞,∞, where f:ℝ4⟶ℝ is continuous and T-periodic in t. …”
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