Longitudinal Vibration and Stability Analysis of Conveying Belt of Belt Conveyor by Man Zhang, Haoxuan Jin, Yongqiang Yang, Yuanhu Cheng, Taisong Guo

“…The differential equation of longitudinal vibration of the belt conveyor with stable conveying speed is established based on Kelvin-Voigt viscoelastic theory. …”
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Analysis of the Thermo-elastic for Involute Spur Gear Transmission with Logarithmic Modification by Jin Tingting, Wang Jiugen, Wang Zhenrong

“…Aiming at the involute spur gear with logarithmic modification,according to the heat conduction differential equation and the basic equations of thermo-elasticity,the thermal and thermo-elastic fields of involute spur gear at any meshing position are obtained by using the FFT and IFFT programming calculation,the influence of the torque and rotational speed on temperature field and thermal elastic field is discussed.The results show that,the logarithmic modification can reduce the strong thermal at the edges of the gear tooth caused by the edge effect,thus the scuffing resistance,accuracy and thermal fatigue life of gears are improved.The rising of either torque or rotational speed can intensify the temperature field and thermo-elastic field of gear,and the modification amount should be designed in terms of torque in order to avoid the edge effect.…”
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Multiple Solutions of Mixed Convective MHD Casson Fluid Flow in a Channel by Jawad Raza, Azizah Mohd Rohni, Zurni Omar

“…Governing partial differential equation of the proposed problem converted into nonlinear ordinary differential equations by using similarity transformation. …”
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Obtaining the Soliton Type Solutions of the Conformable Time-Fractional Complex Ginzburg–Landau Equation with Kerr Law Nonlinearity by Using Two Kinds of Kudryashov Methods by Arzu Akbulut

“…Thus, using the suitable wave transform, the given equation is converted into an ordinary differential equation. Then, the proposed methods are applied to the reduced equation. …”
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Stability of a positive equilibrium state for a stochastically perturbed mathematical model ofglassy-winged sharpshooter population by Leonid Shaikhet

“…A necessary and sufficient condition for asymptotic mean square stability of the equilibrium point of the linear part of the considered stochastic differential equation is obtained. This condition is at the same time a sufficient one for stability in probability of the equilibrium point of the initial nonlinear equation. …”
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Two-Dimensional and Axisymmetric Unsteady Flows due to Normally Expanding or Contracting Parallel Plates by Saeed Dinarvand, Abed Moradi

“…The governing nonlinear equations and their associated boundary conditions are transformed into a highly non-linear ordinary differential equation. The series solution of the problem is obtained by utilizing the homotopy perturbation method (HPM). …”
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Identification of a Stochastic Dynamic Model for Aircraft Flight Attitude Based on Measured Data by Haiquan Li, Xiaoqian Chen, Jiatu Zhang, Bochen Wang, Jiahui Peng, Liang Wang

“…Therefore, a stochastic differential equation for aircraft flight attitude is modeled based on the traditional one in this paper. …”
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Disease dynamics for the hometown of migrant workers by Ram P. Sigdel, C. Connell McCluskey

“…Biol. 300:100--109 (2012) formulatedand studied a delay differential equation model for disease dynamics in a region where a portionof the population leaves to work in a different region for an extended fixed period. …”
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A Simple Distributed RGC Model of MOSFET for Pre-Pinch Off Region by Umesh Kumar, Arun Mirchandani

“…The differential equation describing the small signal behavior of a MOSFET channel is derived. …”
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Analytical Method in Solving Flow of Viscoelastic Fluid in a Porous Converging Channel by M. Esmaeilpour, Naeem Roshan, Negar Roshan, D. D. Ganji

“…An analytical method, called homotopy perturbation method (HPM), is used to compute an approximation to the solution of the nonlinear differential equation governing the problem of two-dimensional and steady flow of a second-grade fluid in a converging channel. …”
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Taking into account the lens geometric distortion during accumulation of blurred star images in an astro-inertial attitude sensor by S. N. Vasilyuk

“…The analytical approach uses a model of direct distortion correction, which makes it possible to obtain a new differential equation for the blur trajectory in the image plane with distortion. …”
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Convergence Time Calculation for Supertwisting Algorithm and Application for Nonaffine Nonlinear Systems by Jianhua Zhang, Quanmin Zhu, Yang Li

“…The convergence time of the STA is provided by calculating the solution of a differential equation instead of constructing Lyapunov function. …”
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Dynamics of a Stage Structured Pest Control Model in a Polluted Environment with Pulse Pollution Input by Bing Liu, Ling Xu, Baolin Kang

“…By using pollution model and impulsive delay differential equation, we formulate a pest control model with stage structure for natural enemy in a polluted environment by introducing a constant periodic pollutant input and killing pest at different fixed moments and investigate the dynamics of such a system. …”
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Quasigeostrophic Equations for Fractional Powers of Infinitesimal Generators by Luciano Abadias, Pedro J. Miana

“…In this paper we treat the following partial differential equation, the quasigeostrophic equation: ∂/∂t+u·∇f=-σ-Aαf,  0≤α≤1, where (A,D(A)) is the infinitesimal generator of a convolution C0-semigroup of positive kernel on Lp(Rn), with 1≤p<∞. …”
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Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem by Wen Lian, Zhanbing Bai

“…The existence and multiplicity of positive solutions for the nonlinear fractional differential equation boundary value problem (BVP) DC0+αyx+fx,yx=0,   0<x<1, y0=y′1=y″0=0 is established, where 2<α≤3,  CD0+α is the Caputo fractional derivative, and f:0,1×0,∞⟶0,∞ is a continuous function. …”
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Positive Solutions for the Initial Value Problems of Fractional Evolution Equation by Yue Liang, Yu Ma, Xiaoyan Gao

“…As an example, we study the partial differential equation of parabolic type of fractional order.…”
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A Class of PDEs with Nonlinear Superposition Principles by Li Peng, Liu Keying, Pan Zuliang, Zhong Weizhou

“…In the end, some applications of the PDEs are explained, which shows that the result has very subtle relations with linearization of partial differential equation.…”
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Generalized Hyperbolic Function Solution to a Class of Nonlinear Schrödinger-Type Equations by Zeid I. A. Al-Muhiameed, Emad A.-B. Abdel-Salam

“…With the help of the generalized hyperbolic function, the subsidiary ordinary differential equation method is improved and proposed to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. …”
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Initial Time Difference Stability of Causal Differential Systems in terms of Lyapunov Functions and Lyapunov Functionals by Coşkun Yakar, Mustafa Bayram Gücen

“…We investigate the qualitative behavior of a perturbed causal differential equation that differs in initial position and initial time with respect to the unperturbed causal differential equations. …”
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INCREMENTAL HARMONIC BALANCE METHOD FOR THE STUDY OF SUPPORT LOOSENESS FAULT’S CHARACTERISTICS by CAO QingSong, XIANG Qin, XIONG GuoLiang

“…To a Jeffcott rotor system with support looseness fault,a vibration differential equation with piecewise-linear stiffness was established by considering the system with one-side support looseness and the rotor with unbalanced extraneous exciting force. …”
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