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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A toxin-mediated size-structured population model: Finite difference approximation and well-posedness by Qihua Huang, Hao Wang

“…Motivated by the fact that individuals with different sizes may have different sensitivities to toxins, we develop a toxin-mediated size-structured model which is given by a system of first order fully nonlinear partial differential equations (PDEs). It is very possible that this work represents the first derivation of a PDE model in the area of ecotoxicology. …”
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Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems by D. Baleanu, A. H. Bhrawy, T. M. Taha

“…We present a direct solution technique for approximating linear multiterm fractional differential equations (FDEs) on semi-infinite interval, using generalized Laguerre polynomials. …”
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Settlement Prediction Based on the Relationship between the Empirical and Analytical Solutions of a Cylindrical Cavity under Undrained Conditions by Pieride Mabe Fogang, Yang Liu, Pengqiang Yu

“…The expansion of the cylindrical cavity is solved as a linear elasticity problem using a system of first-order ordinary differential equations containing two components in the Cartesian coordinates. …”
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Heat Transfer in Boundary Layer Magneto-Micropolar Fluids with Temperature-Dependent Material Properties over a Stretching Sheet by Ephesus O. Fatunmbi, Samuel S. Okoya

“…With the aid of similarity conversion analysis, the formulated equations of the flow and heat transfer have been translated into a system of nonlinear ordinary differential equations. Subsequently, Runge–Kutta–Fehlberg integration scheme in company of shooting techniques employed to obtain numerical solutions to the reduced equations. …”
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The Inverse Problem of Identification of Hydrogen Permeability Model by Yury V. Zaika, Natalia I. Rodchenkova, Ekaterina K. Kostikova

“…A numerical method is developed for TDS spectrum simulation, where only integration of a nonlinear system of low order ordinary differential equations is required. The main final output of the article is a noise-resistant algorithm for solving the inverse problem of parametric identification for the aggregated experiment where desorption and diffusion are dynamically interrelated (without the artificial division of studies into the diffusion limited regime (DLR) and the surface limited regime (SLR)).…”
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Recent Developments on Hybrid Time-Frequency Numerical Simulation Techniques for RF and Microwave Applications by Jorge F. Oliveira, José C. Pedro

“…This apparent multirate behavior can be appropriately described using partial differential equations (PDEs) within a bivariate framework, which can be solved in an efficient way using hybrid time-frequency techniques. …”
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Estimates for Unimodular Multipliers on Modulation Hardy Spaces by Jiecheng Chen, Dashan Fan, Lijing Sun, Chunjie Zhang

“…Finally, we investigate the boundedness of the operator eit|Δ|α/2 for α>0 and obtain the local well-posedness for the Cauchy problem of some nonlinear partial differential equations with fundamental semigroup eit|Δ|α/2.…”
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Discontinuous nonlocal conservation laws and related discontinuous ODEs – Existence, Uniqueness, Stability and Regularity by Keimer, Alexander, Pflug, Lukas

“…This fixed-point problem itself necessitates the study of existence, uniqueness and stability of a class of discontinuous ordinary differential equations. On the ODE level, we compare the solution type defined here with the well-known Carathéodory and Filippov solutions.…”
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Dynamic Model of a Rotating Flexible Arm-Flexible Root Mechanism Driven by a Shaft Flexible in Torsion by S.Z. Ismail, A.A. Al-Qaisia, B.O. Al-Bedoor

“…The obtained model is a nonlinear-coupled system of differential equations. The model is simulated for different combinations of shaft and root flexibilities and arm properties. …”
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Adaptive control of single-input single-output hybrid systems possessing interacting discrete- and continuous-time dynamics by M. de la Sen

“…As a result there are also mixed continuous-time and discrete signals present in the system associated either with the solutions of differential equations which depend at the same time on both discrete-time and continuous-time forcing terms and on generalized difference equations associated with discretized and digital signals. …”
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Static Characteristics of Improved Composite Box Girder with Corrugated Steel Webs by Shijin Wang, Genhui Wang, Zichen Zhang

“…In order to accurately calculate the cross-sectional stresses and deflections of the improved composite box girder with corrugated steel webs, the control differential equations and boundary conditions are established based on the energy variational principle, taking into account the effects of corrugated steel web properties, shear lag, and shear deformation. …”
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Aeroelastic Vibrations and Stability in Cyclic Symmetric Domains by Bernard Lalanne, Maurice Touratier

“…Firstly, general and usual cyclic symmetric properties are recovered from the Floquet theorem for differential equations, having space periodic coefficients in conjunction with a discrete space Fourier series development. …”
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Analysis of an HIV infection model incorporating latency age and infection age by Jinliang Wang, Xiu Dong

“…There is a growing interest to understand impacts of latent infection age and infection age on viral infection dynamics by using ordinary and partial differential equations. On one hand, activation of latently infected cells needs specificity antigen, and latently infected CD4+ T cells are often heterogeneous, which depends on how frequently they encountered antigens, how much time they need to be preferentially activated and quickly removed from the reservoir. …”
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A New Way to Generate an Exponential Finite Difference Scheme for 2D Convection-Diffusion Equations by Caihua Wang

“…The idea of the method can be applied to a wide variety of differential equations.…”
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Generalized Thermopiezoelectricity with Memory-Dependent Derivative and Transient Thermoelectromechanical Responses Analysis by Jianzhong Sun, Yaping Wu

“…In this paper, a novel generalized thermoelastopiezoelectric model is established by introducing memory-dependent derivative, which might be superior to fractional ones: the form is unique, while the fractional-order theories have various expressions with different authors; it is more intuitionistic for reflecting the memory effect; the physical meanings of the related memory-dependent differential equations are more clear, which are determined by the essence of their definitions; the time-delay and kernel function can be chosen freely based on the necessity of practical applications. …”
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Adaptive Synchronization for Two Different Stochastic Chaotic Systems with Unknown Parameters via a Sliding Mode Controller by Zengyun Wang, Lihong Huang, Xuxin Yang, Dingyang Lu

“…Firstly, based on the Lyapunov theory in stochastic differential equations and the theory of sliding mode control, we propose a simple sliding surface and discuss the occurrence of the sliding motion. …”
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Adaptive Time-Stepping Using Control Theory for the Chemical Langevin Equation by Silvana Ilie, Monjur Morshed

“…This model is represented as a system of stochastic differential equations, with multiplicative and noncommutative noise. …”
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Global Dynamics of Secondary DENV Infection with Diffusion by A. M. Elaiw, A. S. Alofi

“…In this study, we develop and investigate a partial differential equations (PDEs) model that describes the dynamics of secondary DENV infection taking into account the spatial mobility of DENV particles and cells. …”
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