A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams by Nicholas H. Erdelyi, Seyed M. Hashemi

“…Using the Euler-Bernoulli bending beam theory, the governing differential equations are exploited and representative, frequency-dependent, field variables are chosen based on the closed form solution to these equations. …”
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Forced Vibration of Delaminated Timoshenko Beams under the Action of Moving Oscillatory Mass by M.H. Kargarnovin, M.T. Ahmadian, R.A. Jafari-Talookolaei

“…To solve the governing differential equations of motion using modal expansion series, eigen-solution technique is used to obtain the natural frequencies and their corresponding mode shapes necessary for forced vibration analysis. …”
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Assessing the global dynamics of Nipah infection under vaccination and treatment: A novel computational modeling approach. by Fang Yu, Muhammad Younas Khan, Muhammad Bilal Riaz, Saif Ullah, Muhammad Farooq

“…Initially, the model includes nine nonlinear ordinary differential equations that consider viral concentration, flying fox, and human populations simultaneously. …”
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The global stability of an SIRS model with infection age by Yuming Chen, Junyuan Yang, Fengqin Zhang

“…In this paper, we consider an SIRS modelwith infection age, which is described by a mixed system ofordinary differential equations and partial differentialequations. …”
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A New Fractional Model for Cancer Therapy with M1 Oncolytic Virus by Majda El Younoussi, Zakaria Hajhouji, Khalid Hattaf, Noura Yousfi

“…The aim of this work is to propose and analyze a new mathematical model formulated by fractional differential equations (FDEs) that describes the dynamics of oncolytic M1 virotherapy. …”
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Common Fixed-Point Results in Ordered Left (Right) Quasi-b-Metric Spaces and Applications by Hemant Kumar Nashine, Sourav Shil, Hiranmoy Garai, Lakshmi Kanta Dey, Vahid Parvaneh

“…Further, we use our results to establish sufficient conditions for existence and uniqueness of solution of a system of nonlinear matrix equations and a pair of fractional differential equations. Finally, we provide a nontrivial example to validate the sufficient conditions for nonlinear matrix equations with numerical approximations.…”
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Graph-theoretic conditions for zero-eigenvalue Turing instability in general chemical reaction networks by Maya Mincheva, Gheorghe Craciun

“…If the SR graph satisfies certain conditions, similar to the conditions for ruling out multiple equilibria in spatially homogeneous differential equations systems, then the corresponding mass-action reaction-diffusion system cannot exhibit zero-eigenvalue Turing instability for any parameter values.On the other hand, if the graph-theoretic condition for ruling out zero-eigenvalue Turing instability is not satisfied, then the corresponding model may display zero-eigenvalue Turing instability for some parameter values. …”
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Discrete Approaches to Continuous Boundary Value Problems: Existence and Convergence of Solutions by Douglas R. Anderson, Christopher C. Tisdell

“…Firstly, we study BVPs that involve nonlinear difference equations (the “discrete” BVP); and secondly, we study BVPs involving nonlinear ordinary differential equations (the “continuous” BVP). We formulate some sufficient conditions under which the discrete BVP will admit solutions. …”
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Modeling the motion of a ship with suspended cargo by Solovyov A. A., Shugay S. N.

“…When solving problems of dynamics, mathematical models of the roll of a vessel with suspended cargo in calm water and regular waves have been proposed, and linear differential equations of the roll of a vessel with suspended cargo have been obtained. …”
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Nonlinear Vibration of a Continuum Rotor with Transverse Electromagnetic and Bearing Excitations by Haiyang Luo, Yuefang Wang

“…The governing equation of motion is derived and discretized as a group of ordinary differential equations using the Galerkin's method. The stability of the equilibrium of the rotor is analyzed with the Routh-Hurwitz criterion and the occurrence of the Andronov-Hopf bifurcation is pointed out. …”
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Dynamic Response of Shear-Flexible Cylindrical Isotropic Shells with Clamped Edges by Zafer I. Sakka, Jamal A. Abdalla, H.R.H. Kabir

“…The Sander’s kinematic relations for moderately thick cylindrical shell panels are utilized to develop the governing partial differential equations in conjunction with the boundary conditions. …”
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Qualitative Analysis of the Effect of Weeds Removal in Paddy Ecosystems in Fallow Season by Leru Zhou, Zhigang Liu, Tiejun Zhou

“…In the paper, we introduce a differential equations model of paddy ecosystems in the fallow season to study the effect of weeds removal from the paddy fields. …”
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Noether and partial Noether approach for the nonlinear (3+1)-dimensional elastic wave equations. by Akhtar Hussain, M Usman, Fiazuddin Zaman, Ahmed M Zidan, Jorge Herrera

“…The Lie group method is a powerful technique for obtaining analytical solutions for various nonlinear differential equations. This study aimed to explore the behavior of nonlinear elastic wave equations and their underlying physical properties using Lie group invariants. …”
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Studies on the Effects of Interphase Heat Exchange during Thermal Explosion in a Combustible Dusty Gas with General Arrhenius Reaction-Rate Laws by K. S. Adegbie, F. I. Alao

“…The equations governing the physical model with realistic assumptions are stated and nondimensionalised leading to an intractable system of first-order coupled nonlinear differential equations, which is not amenable to exact methods of solution. …”
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Numerical analysis of the self-sustaining traveling wave of nuclear fission propagated by epithermal neutrons in uranium dicarbide medium by M. R. Shcherbyna, K. O. Shcherbyna, V. O. Tarasov, S. I. Kosenko, S. A. Chernezhenko

“…This study investigates the self-sustaining traveling wave of nuclear fission in a uranium dicarbide medium by numerically solving a system of partial differential equations. The primary focus is on the neutron diffusion equation and nuclide balance equations, which are crucial for understanding the behavior of fission waves. …”
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Novel Evaluation of Fuzzy Fractional Helmholtz Equations by Meshari Alesemi, Naveed Iqbal, Noorolhuda Wyal

“…It is critical to emphasize that the purpose of the proposed fuzziness approach is to demonstrate the efficiency and superiority of numerical solutions to nonlinear fractional fuzzy partial differential equations that arise in complex and physical structures.…”
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Some Properties of Motion Equations Describing the Nonlinear Dynamical Response of a Multibody System with Flexible Elements by Maria Luminiţa Scutaru, Sorin Vlase

“…Finally, second-order differential equations with variable coefficients are obtained; these equations are strong nonlinear ones due to the time-dependent values of angular speed and acceleration, and they can be linearized considering a very short period of time, in which the motion is considered to be “frozen.” …”
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Investigation of Nonlinear Vibrational Analysis of Circular Sector Oscillator by Using Cascade Learning by Naveed Ahmad Khan, Muhammad Sulaiman, Jamel Seidu, Fahad Sameer Alshammari

“…This paper analyzed the model of swinging oscillation of a solid circular sector arising in hydrodynamical machines, electrical engineering, heat transfer applications, and civil engineering. Nonlinear differential equations govern the mathematical model for frequency oscillation of the system. …”
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Opposition to Synchronization of Bistable State in Motif Configuration of Rössler Chaotic Oscillator Systems by Dıdıer Lopez Mancılla, Guillermo Huerta-cuellar, Juan Hugo García López, Rider Jaimes-reategui

“…The study was conducted using the differential equations representing the piecewise linear Rössler-like electronic circuits; the initial conditions were changed to achieve a bistable characteristic Homoclinic H-type or Rössler R-type attractor. …”
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Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems by Hammad Khalil, Mohammed Al-Smadi, Khaled Moaddy, Rahmat Ali Khan, Ishak Hashim

“…The paper is devoted to the study of operational matrix method for approximating solution for nonlinear coupled system fractional differential equations. The main aim of this paper is to approximate solution for the problem under two different types of boundary conditions, m^-point nonlocal boundary conditions and mixed derivative boundary conditions. …”
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