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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Dynamics of a plant-herbivore model with toxin-induced functional response by Ya Li, Z. Feng

“…Themodel consists of three ordinary differential equations describingone herbivore population and two plant species with differenttoxicity levels. …”
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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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An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges by Xue Kai, Wang Jiufa, Li Qiuhong, Wang Weiyuan, Wang Ping

“…The matrix eigenvalue equation which is equivalent to governing differential equations of the plate can be derived through using the boundary conditions and the governing equations based on Mindlin plate theory. …”
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Raves, clubs and ecstasy: the impact of peer pressure by Baojun Song, Melissa Castillo-Garsow, Karen R. Ríos-Soto, Marcin Mejran, Leilani Henso, Carlos Castillo-Chavez

“…In this study, a system of differential equations is used to model the peer-driven dynamics of ecstasy use. …”
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Mathematical Modelling of Malaria Disease Transmission and Control. by Muhangi, Benard

“…The deterministic compartmental model was examined using stability theory of differential equations. The reproduction number was obtained to be asymptotically stable conditions for the disease-free, and the endemic equilibria were determined. …”
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On the Regularity of the Entropy Solution of the Fractional-Semigeostrophic Equation Using Ultrafilters by Gilles Tamba Bokolo

“…This work lays the groundwork for future studies on fractional partial differential equations in geophysical contexts, potentially leading to more accurate predictive models in meteorology and oceanography.…”
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Mathematical Model for Thermal Processes of Single-Core Power Cable by D. I. Zalizny, S. N. Prohorenko

“…Thermal processes between homogeneous bodies are described by a system of four differential equations. The paper contains a proposal to solve this system of equations with the help of a thermal equivalent circuit and the Laplace transform. …”
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Computational Modelling of Blood Flow Development and Its Characteristics in Magnetic Environment by Gopal Chandra Shit

“…The governing coupled nonlinear differential equations of magnetohydrodynamic (MHD) fluid flow are reduced to a nondimensional form, which are then characterized by four dimensionless parameters. …”
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Topology in nonlinear extensions of hypernumbers by M. S. Burgin

“…Modern theory of dynamical systems is mostly based on nonlinear differential equations and operations. At the same time, the theory of hypernumbers and extrafunctions, a novel approach in functional analysis, has been limited to linear systems. …”
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Modeling Multicellular Systems Using Subcellular Elements by T. J. Newman

“…We present here a detailed description of the model, and use successive mean-field approximations to connect it to more coarse-grained approaches, such as discrete cell-based algorithms and coupled partial differential equations. We also discuss efficient algorithms for encoding the model, and give an example of a simulation of an epithelial sheet. …”
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Dynamic Effective Properties of Lead-Reinforced Epoxy Resin Composites with Differential Method by Haitao Zhu, Yongping Wan

“…The corresponding differential equations are numerically solved by the fourth-order Runge–Kutta method, and the dynamic effective modulus and density are obtained. …”
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Vibrations of a Simply Supported Beam with a Fractional Viscoelastic Material Model – Supports Movement Excitation by Jan Freundlich

“…This assumption simplifies solution of the fractional differential equations and enables us to directly obtain amplitude-frequency characteristics of the examined system. …”
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Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics by Haileyesus Tessema Alemneh

“…In this paper, a nonlinear deterministic model for the dynamics of corruption is proposed and analysed qualitatively using the stability theory of differential equations. The basic reproduction number with respect to the corruption-free equilibrium is obtained using next-generation matrix method. …”
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A Bright Entanglement and Squeezing Generated by an External Pumping Radiation in a Correlated Emission Laser by Chimdessa Gashu

“…The quantum and statistical properties of light generated by an external classical field in a correlated emission laser with a parametric amplifier and coupled to a squeezed vacuum reservoir are investigated using the combination of the master and stochastic differential equations. First, the solutions of the cavity-mode variables and correlation properties of noise forces associated to the normal ordering are obtained. …”
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Probability Density Evolution Algorithm for Stochastic Dynamical Systems Based on Fractional Calculus by Yang Yan, Xiaohong Yu

“…Dynamical models of the dynamic system and coupled system “three-car vehicle-rail-bridge” are established, the time-varying differential equations of motion are derived in detail, and the dynamic response of the system is calculated using the explicit Newmark algorithm. …”
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Review on Mathematical and Mechanical Models of the Vocal Cord by L. Cveticanin

“…The corresponding mathematical models are the systems of coupled second-order differential equations which describe the vibrations of the symmetric and asymmetric vocal folds. …”
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Application of Local Fractional Homotopy Perturbation Method in Physical Problems by Nabard Habibi, Zohre Nouri

“…Most physical phenomena are modeled according to partial differential equations. It is difficult for nonlinear models to obtain the closed form of the solution, and in many cases, only an approximation of the real solution can be obtained. …”
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A Novel Method for Constructing Grid Multi-Wing Butterfly Chaotic Attractors via Nonlinear Coupling Control by Yun Huang

“…Based on the three-dimensional Lorenz system, two first-order differential equations are added along with one linear coupling controller, respectively. …”
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Recent Developments on Operator-Difference Schemes for Solving Nonlocal BVPs for the Wave Equation by Mehmet Emir Koksal

“…Two new second-order difference schemes recently appeared in the literature are compared numerically with each other and with the rather old first-order difference scheme all to solve abstract Cauchy problem for hyperbolic partial differential equations with time-dependent unbounded operator coefficient. …”
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