Dynamics Simulation of the Tooth Root Crack Fault of Gear Transmission System by Ning Shaohui, Han Zhennan, Li Yuexian, Wu Xuefeng

“…By using the Matlab,the dynamics differential equations of the model are solved,the angular velocity and angular acceleration simulation curve of the two kinds of fault and intact gear are got,the result is that the gear turning crack,angular velocity and angular acceleration of the driven produced obvious fluctuations,the calculation results are consistent with theoretical analysis.…”
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Sensitivity and Optimal Control Analysis of an Extended SEIR COVID-19 Mathematical Model by C. M. Wachira, G. O. Lawi, L. O. Omondi

“…In this paper, a mathematical model based on a system of ordinary differential equations is developed with vaccination as an intervention for the transmission dynamics of coronavirus 2019 (COVID-19). …”
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Novel exact solutions for PDEs with mixed boundary conditions by Mark Craddock, Martino Grasselli, Andrea Mazzoran

“…Abstract We develop methods for the solution of inhomogeneous Robin-type boundary value problems (BVPs) that arise for certain linear parabolic partial differential equations (PDEs) on a half-line, as well as a second-order generalization. …”
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Analysis of the Nonlinear Structural-Acoustic Resonant Frequencies of a Rectangular Tube with a Flexible End Using Harmonic Balance and Homotopy Perturbation Methods by Y. Y. Lee

“…The structural acoustic problem considered in this study is the nonlinear resonant frequencies of a rectangular tube with one open end, one flexible end, and four rigid side walls A multiacoustic single structural modal formulation is derived from two coupled partial differential equations which represent the large amplitude structural vibration of the flexible end and acoustic pressure induced within the tube. …”
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Physics Informed by Deep Learning: Numerical Solutions of Modified Korteweg-de Vries Equation by Yuexing Bai, Temuer Chaolu, Sudao Bilige

“…The method that we used in this paper had demonstrated the powerful mathematical and physical ability of deep learning to flexibly simulate the physical dynamic state represented by differential equations and also opens the way for us to understand more physical phenomena later.…”
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A Study of a Diseased Prey-Predator Model with Refuge in Prey and Harvesting from Predator by Ahmed Sami Abdulghafour, Raid Kamel Naji

“…The proposed mathematical model is consisting of three first-order nonlinear ordinary differential equations, which describe the interaction among the healthy prey, infected prey, and predator. …”
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THE RESEARCH OF LOCAL STABILITY FOR SIMPLY SUPPORTED SKEW PLATES IN THE CRANE by FU WeiGang, YAN Feng, LI Meng, CHENG WenMing

“…To study the buckling of bionics skew plates in the crane’s vein box girder,the dimensionless derivations of bucking balance differential equations for skew plates has been given when it is affected by the longitudinal load in the oblique coordinate,and the dimensionless equation of boundary conditions is also given. …”
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Existence of a unique solution to a fourth-order boundary value problem and elastic beam analysis by Ravindra Rao, Jagan Mohan Jonnalagadda

“…We study the existence and uniqueness of solutions to a particular class of two-point boundary value problems involving fourth-order ordinary differential equations. Such problems have exciting applications for modeling the deflections of beams. …”
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On the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable Methods by A. K. Gupta, S. Saha Ray

“…Haar wavelet method is an efficient numerical method for the numerical solution of arbitrary order partial differential equations like Burgers-Fisher and generalized Fisher equations. …”
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Mixed Convection over an Inclined Wavy Surface in a Nanofluid Saturated Non-Darcy Porous Medium with Radiation Effect by Darbhasayanam Srinivasacharya, Poshala Vijay Kumar

“…The governing equations are transformed into a set of ordinary differential equations using the appropriate similarity transformation and then solved using the successive linearization method. …”
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Convertible Bonds with Higher Loan Rate: Model, Valuation, and Optimal Strategy by Haiyang Wang, Zhen Wu

“…We study the pricing problem for convertible bonds via backward stochastic differential equations (BSDEs). By virtue of reflected BSDEs and Malliavin derivatives, we establish the formulae for the fair price of convertible bonds and the hedging portfolio strategy explicitly. …”
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Vibration Suppression of a Coupled Aircraft Wing with Finite-Time Convergence by Yiming Liu, Zhifeng Tan, Xiaofen Yang, Xiaowei Wang

“…Since the model is modeled by partial differential equations, the traditional control design scheme based on the ordinary differential equation model is not applicable, and the control law design becomes very complex. …”
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Novel Stability Criteria of Nonlinear Uncertain Systems with Time-Varying Delay by Yali Dong, Shengwei Mei, Xueli Wang

“…By constructing the proposed Lyapunov-Krasovskii functional approach, continuous state feedback controllers are put forward, and the criteria which guarantee the exponential stabilization of the nonlinear systems with uncertainties and time-varying delay are established in terms of solutions to the standard Riccati differential equations. Furthermore, based on the Lyapunov method and the linear matrix inequality approach, the sufficient conditions of exponential stability for a class of uncertain systems with time-varying delays and nonlinear perturbations are derived. …”
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Pseudo-State Sliding Mode Control of Fractional SISO Nonlinear Systems by Bao Shi, Jian Yuan, Chao Dong

“…Firstly, a stable fractional sliding mode surface is constructed based on the Routh-Hurwitz conditions for fractional differential equations. Secondly, a sliding mode control law is designed using the theory of Mittag-Leffler stability. …”
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Traveling Wave Solutions of Space-Time Fractional Generalized Fifth-Order KdV Equation by Dianchen Lu, Chen Yue, Muhammad Arshad

“…At the end, three types of exact traveling wave solutions are obtained which indicate that the method is very practical and suitable for solving nonlinear fractional partial differential equations.…”
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Solving Quantum Dynamics with a Lie-Algebra Decoupling Method by Sofia Qvarfort, Igor Pikovski

“…The approach involves identifying a Lie algebra that governs the dynamics of the system, enabling the derivation of differential equations to solve the Schrödinger equation. …”
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Group Classification of a Generalized Lane-Emden System by Ben Muatjetjeja, Chaudry Masood Khalique, Fazal Mahmood Mahomed

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Stability Analysis of a Class of Neural Networks with State-Dependent State Delay by Yue Chen, Jin-E Zhang

“…The differential equations with state-dependent delay are very important equations because they can describe some problems in the real world more accurately. …”
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Vibrations of Plates and Shells with Attached Mass by L. U. Sultanov, I. R. Garifullin

“…The transition from the initial dynamic system to the solution of the final system of nonlinear ordinary differential equations was achieved by the Bubnov–Galerkin method. …”
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The Approximate Solution of Some Plane Boundary Value Problems of the Moment Theory of Elasticity by Roman Janjgava

“…We consider a two-dimensional system of differential equations of the moment theory of elasticity. …”
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