Dynamic Responses of an Overhead Crane’s Beam Subjected to a Moving Trolley with a Pendulum Payload by Huasen Liu, Wenming Cheng, Yinqi Li

“…In this paper, the coupling system of an overhead crane was simplified to that of a moving mass with pendulum swing passing beam model. The differential equation motion of a coupled overhead crane system was derived based on the Lagrange equation. …”
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Modified Homotopy Perturbation Method and Approximate Solutions to a Class of Local Fractional Integrodifferential Equations by Bo Xu, Sheng Zhang

“…In this paper, the local fractional version of homotopy perturbation method (HPM) is established for a new class of local fractional integral-differential equation (IDE). With the embedded homotopy parameter monotonously changing from 0 to 1, the special easy-to-solve fractional problem continuously deforms to the class of local fractional IDE. …”
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-Advanced Models for Tsunami and Rogue Waves by D. W. Pravica, N. Randriampiry, M. J. Spurr

“…A wavelet , that satisfies the q-advanced differential equation for , is used to model N-wave oscillations observed in tsunamis. …”
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Analysis of a Coupled System of Nonlinear Fractional Langevin Equations with Certain Nonlocal and Nonseparated Boundary Conditions by Zaid Laadjal, Qasem M. Al-Mdallal, Fahd Jarad

“…In this article, we use some fixed point theorems to discuss the existence and uniqueness of solutions to a coupled system of a nonlinear Langevin differential equation which involves Caputo fractional derivatives of different orders and is governed by new type of nonlocal and nonseparated boundary conditions consisting of fractional integrals and derivatives. …”
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Uniformly Convergent Nonpolynomial Spline Method for Singularly Perturbed Robin-Type Boundary Value Problems with Discontinuous Source Term by Habtamu Garoma Debela, Gemechis File Duressa

“…In this paper, a singularly perturbed second-order ordinary differential equation with discontinuous source term subject to mixed-type boundary conditions is considered. …”
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VIBRATION MODAL ANALYSIS AND RESEARCH OF CANTILEVER BEAM BASED ON POLY IIR METHOD by ZHANG Min, ZHANG Yi, HOU YaoHua, MA GuangXuan

“…Following to use Bernoulli Euler beam theory to calculate the beam vibration differential equation,in addition to the beam set specific boundary constraint conditions to calculate each order modal parameters,using the Workbench beam finite element simulation analysis for the first five order natural frequency and vibration mode. …”
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Resonance Spectra of Caged Stringy Black Hole and Its Spectroscopy by I. Sakalli, G. Tokgoz

“…We then show how the complex resonant frequencies of the caged GHSBH are computed using the Bessel differential equation that arises when the scalar perturbations around the event horizon are considered. …”
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Multiple Nonlinear Oscillations in a 𝔻3×𝔻3-Symmetrical Coupled System of Identical Cells with Delays by Haijun Hu, Li Liu, Jie Mao

“…The individual cells are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. …”
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Asymptotic Behavior of an Optimal Investment-Reinsurance Problem with General Utility Functions by Yan Zhang, Peibiao Zhao

“…Moreover, applying the dual method along with the partial differential equation method, we verify the asymptotic behavior of the optimal control strategy, which means that the optimal investment-reinsurance strategy with the general utility functions converges to that with the power utility function at any level of the initial wealth.…”
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Global attractivity of positive periodic solutions for an impulsive delay periodic food limited population model by Jian Song

“…We will consider the following nonlinear impulsive delay differential equation N′(t)=r(t)N(t)((K(t)−N(t−mw))/(K(t)+λ(t)N(t−mw))), a.e. t>0, t≠tk, N(tk+)=(1+bk)N(tk), K=1,2,…, where m is a positive integer, r(t), K(t), λ(t) are positive periodic functions of periodic ω. …”
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Numerical Solutions to Optimal Portfolio Selection and Consumption Strategies under Stochastic Volatility by Lei Ge, Qiang Zhang

“…Based on the method of dynamic programming, this paper uses analysis methods governed by the nonlinear and inhomogeneous partial differential equation to study modern portfolio management problems with stochastic volatility, incomplete markets, limited investment scope, and constant relative risk aversion (CRRA). …”
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Coefficients of prolongations for symmetries of ODEs by Ricardo Alfaro, Jim Schaeferle

“…He found that transformations which form a continuous group and leave a differential equation invariant can be used to simplify the equation. …”
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Traverse Vibration of Axially Moving Laminated SMA Beam considering Random Perturbation by Hao Ying, Gao Minglei

“…The transverse vibration differential equation of axially moving SMA laminated beam with two simply-supported edges is obtained through the Galerkin method. …”
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Finiteness of rank for Grassmann convexity by Saldanha, Nicolau, Shapiro, Boris, Shapiro, Michael

“…The Grassmann convexity conjecture, formulated in [8], gives a conjectural formula for the maximal total number of real zeroes of the consecutive Wronskians of an arbitrary fundamental solution to a disconjugate linear ordinary differential equation with real time. The conjecture can be reformulated in terms of convex curves in the nilpotent lower triangular group. …”
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Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems by Mohamed Hannabou, Khalid Hilal, Ahmed Kajouni

“…In this paper, a class of nonlocal impulsive differential equation with conformable fractional derivative is studied. …”
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Mechanism Kinematics Analysis of Two-leg Shield Hydraulic Support by Wang Hongwei, Dong Zhifeng

“…As a multi-linkage mechanism with multi-degree of freedom,the two-leg shield hydraulic support is comprised of beams,fore and rear links and hydraulic cylinders.It can realize supporting roof,protecting coal wall and moving forward under the function of hydraulic power,and plays an important role in coal mining.According to structure and operating characteristics of the two-leg shield hydraulic support,the geometrical relationship and calculations about rear link angle and shield beam angle for the supporting height,head distance,leg length and balance cylinder length are deduced.The differential equation of motion for the hydraulic support is established by the Lagrangian theory,and the support type of ZY17300/32/70 is calculated and analyzed.The relationship between angle displacement and velocity for the rear link angle and shield beam angle along with the motion characteristic of supporting height is obtained.The response characteristics of motion velocity and acceleration for top beam are discussed during the working process of lifting up and down.…”
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Theoretical Vibration Analysis Regarding Excitation due to Elliptical Shaft Journals in Sleeve Bearings of Electrical Motors by Ulrich Werner

“…The solution of the linear differential equation system leads to the mathematical description of the movement of the rotor mass, the shaft journals, and the sleeve bearing housings. …”
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Optimal Strategies for Control of COVID-19: A Mathematical Perspective by Baba Seidu

“…A deterministic ordinary differential equation model for SARS-CoV-2 is developed and analysed, taking into account the role of exposed, mildly symptomatic, and severely symptomatic persons in the spread of the disease. …”
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The discontinuous solutions of Lame�s equations for a conical defect by O. Reut, N. Vaysfeld

“…A discontinuous solution of a certain differential equation in the partial derivatives is a solution that satisfies this equation throughout the region of determining an unknown function, with the exception of the defect points. …”
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Quantum Tunnelling for Hawking Radiation from Both Static and Dynamic Black Holes by Subenoy Chakraborty, Subhajit Saha

“…It is found that different order correction terms satisfy identical differential equation and are solved by a typical technique. …”
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