Diversity and Regularity of Periodic Impact Motions of a Mechanical Vibration System with Multiple Rigid Stops by Fengwei Yin, Guanwei Luo, Xueming Wang

“…The judgment conditions and differential equations of motion of the system masses impacting rigid stops were analyzed. …”
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Some Novel Solutions to a Quadratically Damped Pendulum Oscillator: Analytical and Numerical Approximations by Alvaro H. Salas, Wedad Albalawi, M. R. Alharthi, S. A. El-Tantawy

“…In this paper, some novel analytical and numerical techniques are introduced for solving and analyzing nonlinear second-order ordinary differential equations (ODEs) that are associated to some strongly nonlinear oscillators such as a quadratically damped pendulum equation. …”
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Dynamical Behavior and Stability Analysis in a Stage-Structured Prey Predator Model with Discrete Delay and Distributed Delay by Chao Liu, Qingling Zhang

“…According to Hopf bifurcation theorem for functional differential equations, it can be found that model undergoes Hopf bifurcation around the interior equilibrium when local stability switch occurs and corresponding stable limit cycle is observed. …”
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New Exact Solutions of Kolmogorov Petrovskii Piskunov Equation, Fitzhugh Nagumo Equation, and Newell-Whitehead Equation by Yu-Ming Chu, Shumaila Javeed, Dumitru Baleanu, Sidra Riaz, Hadi Rezazadeh

“…This work presents the new exact solutions of nonlinear partial differential equations (PDEs). The solutions are acquired by using an effectual approach, the first integral method (FIM). …”
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Numerical and analytical approach to the Chandrasekhar quadratic functional integral equation using Picard and Adomian decomposition methods by Eman A. A. Ziada, Hind Hashem, Asma Al-Jaser, Osama Moaaz, Monica Botros

“…This research aimed to find numerical solutions to a type of nonlinear initial value problem (IVP) for hybrid fractional differential equations. Using the Adomian decomposition method (ADM) and the Picard method (PM), we studied the Chandrasekhar quadratic integral equation (QIE). …”
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Analysis of Slippage Characteristic of Roller in Cylindrical Roller Bearing during the Start up by Jia Yongchuan, Deng Sier

“…Based on the dynamics theory of rolling bearing,the dynamics model and nonlinear dynamics differential equations of the cylindrical roller bearing during the start up are obtained by considering of the change of lubrication state between rollers and rings. …”
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Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets by Ai-Min Yang, Yu-Zhu Zhang, Carlo Cattani, Gong-Nan Xie, Mohammad Mehdi Rashidi, Yi-Jun Zhou, Xiao-Jun Yang

“…The obtained results show the simplicity and efficiency of the present technique with application to the problems of the liner differential equations on Cantor sets.…”
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Analysis of the Financial Chaotic Model with the Fractional Derivative Operator by Mamadou Diouf, Ndolane Sene

“…Numerical discretization for the fractional differential equations is applied to the chaotic financial model described by the Caputo derivative. …”
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Stability Analysis of Pneumatic Cabin Pressure Regulating System with Complex Nonlinear Characteristics by Xinhua Zheng, Lili Xie, Lizhuo Liu

“…The governing equations of the considered system consist of 8 differential equations. In the circumstance, commonly used methods of nonlinear system analysis are not applicable. …”
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Effective Method for Analysis of Electrothermally Coupled Fields by Jacek Korytkowski, Stanisław Wincenciak

“…An effective method is presented for solving a nonlinear system of partial differential equations that describe the time-dependent electrothermally coupled fields for passage of constant electric current in a three-dimensional conductive medium. …”
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Application of Soft Computing Paradigm to Large Deformation Analysis of Cantilever Beam under Point Load by Yanmei Cui, Yong Hong, Naveed Ahmad Khan, Muhammad Sulaiman

“…The model is governed by nonlinear differential equations. Large deformation of a cantilever beam has number of applications is structural engineering. …”
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Non Linear Thermal Radiation Analysis of Electromagnetic Chemically Reacting Ternary Nanofluid Flow over a Bilinear Stretching Surface by Shobha V, Hasan Mulki, Baskar P, S. Suresh Kumar Raju, Saleh Mahmoud, Mostafa Abdrabboh, S.V.K. Varma

“…Methodology: The governing nonlinear partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using similarity transformations. …”
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ANN-based two hidden layers computational procedure for analysis of heat transport dynamics in polymer-based trihybrid Carreau nanofluid flow over needle geometry by Adil Darvesh, Fethi Mohamed Maiz, Basma Souayeh, Luis Jaime Collantes Santisteban, Hakim AL. Garalleh, Afnan Al Agha, Lucerito Katherine Ortiz García, Nicole Anarella Sánchez-Miranda

“…These governing system is transformed into ordinary differential equations (ODEs) via appropriate similarity transformations. …”
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Role of stability analysis and waste discharge concentration of ternary hybrid nanofluid in a non-Newtonian model with slip boundary conditions by Nurhana Mohamad, Shuguang Li, Umair Khan, Anuar Ishak, Ali Elrashidi, Mohammed Zakarya

“…The suitable similarity transformations are utilized to transform the partial differential equations (PDEs) into ordinary differential equations (ODEs). …”
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Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System by Alejandro Marquez, Jairo José Espinosa Oviedo, Darci Odloak

“…Around these optimal profiles, the nonlinear partial differential equations (PDEs), that model the reactor are linearized, and afterwards the linear PDEs are discretized in space giving as a result a high-order linear model. …”
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Synchronization of a Supply Chain Model with Four Chaotic Attractors by Jing Zheng, Qiongxin Zhang, Qi Xu, Fei Xu, Victor Shi

“…In this article, we construct a three-stage supply chain model using a system of differential equations to reveal the interplay among producers, distributors, and end customers. …”
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THERMO-MAGNETO-ELASTIC ANALYSIS IN A CURRENT-CARRYING SHELL WITH CLAMPED PERIMETERS by BIAN YuHong, ZHANG Chen

“…The nonlinear partial differential equations including 10 basic unknown variables were established.Using Newmark’s stable finite equidifferent formulas,normal type which can be solved by the discrete-orthogonalization method was obtained. …”
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An extension of Gompertzian growth dynamics: Weibull and Fréchet models by J. Leonel Rocha, Sandra M. Aleixo

“…These models, described by differential equations, are proportional to the hyper-Gompertz growth model. …”
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Analysis of Complex Modal Characteristics of Fractional Derivative Viscoelastic Rotating Beams by Tianle Lu, Zhongmin Wang, Dongdong Liu

“…For the transverse vibration problem of a fractional derivative viscoelastic rotating beam, the differential equation of the system is obtained based on the Euler–Bernoulli beam theory and Hamilton principle. …”
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Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators by Dongyuan Liu, Zigen Ouyang, Huilan Wang

“…Using Banach contraction mapping principle and Leray-Schauder continuation principle, we obtain some sufficient conditions for the existence and uniqueness of the positive solutions for the above fractional order differential equations, which extend some references.…”
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