Second-Order Systems of ODEs Admitting Three-Dimensional Lie Algebras and Integrability by Muhammad Ayub, Masood Khan, F. M. Mahomed

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A frictional contact problem with normal damped response conditions and thermal effects for a thermo-electro-viscoelastic material by Abdelmoumene Djabi

“…The author establishes the existence of a unique weak solution to the problem by utilizing classical results for evolutionary quasivariational elliptic inequalities, parabolic differential equations and fixed point arguments. Design/methodology/approach – The author establishes a variational formulation for the model and proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments. …”
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On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China by Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger

“…In 1986, a mathematical model based on ordinary differential equations was introduced to take into account the distribution of sexual activity. …”
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Predictive Model for Deformation of Adjacent Pipelines Caused by Tunnel Boring in Twin-Lane Tunnels in Soft Ground Layers by Kezhong Wang, Qianjiang Zheng, Maowen Hang

“…To create a discretized prediction model for the deformation of an adjacent pipeline, the pipeline structure is discretized, the differential equations governing the longitudinal deformation of the pipeline are inferred, and the displacement expressions and the solution methods of the virtual nodes of each unit are provided after discretization. …”
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Development of an information measuring and control system for a quadrocopter by V. V. Sleptsov, V. L. Afonin, A. E. Ablaeva, Ba Phuong Dinh

“…The coordinate systems (fixed and mobile) and the kinematic scheme are given, according to which a system of differential equations is presented. The system describes the dynamics of the quadrocopter movement and takes into account the expected smooth movement of the quadrocopter with small roll and pitch angles. …”
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Analysis of non scalar control problems for parabolic systems by the block moment method by Boyer, Franck, Morancey, Morgan

“…We also deduce estimates on the cost of controllability when the final time goes to the minimal null control time.We illustrate how the method works on a few examples of such abstract controlled systems and then we deal with actual coupled systems of one dimensional parabolic partial differential equations. Our strategy enables us to tackle controllability issues that seem out of reach by existing techniques.…”
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Electromagnetic Low-Frequency Dipolar Excitation of Two Metal Spheres in a Conductive Medium by Panayiotis Vafeas, Polycarpos K. Papadopoulos, Dominique Lesselier

“…The calculation of the exact solutions, satisfying Laplace’s and Poisson’s differential equations, leads to infinite linear systems, solved approximately within any order of accuracy through a cut-off procedure and via numerical implementation. …”
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Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filtering by Gerasimos G. Rigatos, Efthymia G. Rigatou, Jean Daniel Djida

“…The intracellular protein synthesis dynamic model is described by a set of coupled nonlinear differential equations. It is shown that such a dynamical system satisfies differential flatness properties and this allows to transform it, through a change of variables (diffeomorphism), to the so-called linear canonical form. …”
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Exploring the Inducement for Social Awareness Behavior and Optimal Control Strategy on Nipah Virus Transmission by Saima Efat, K. M. Ariful Kabir

“…We employ a system of nonlinear ordinary differential equations to dissect how the dynamics of primary infections impact the spread of Nipah disease. …”
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Solving Parabolic and Hyperbolic Equations with Variable Coefficients Using Space-Time Localized Radial Basis Function Collocation Method by Mohammed Hamaidi, Ahmed Naji, Ahmed Taik

“…The advantages of such formulation are (i) time discretization as implicit, explicit, θ-method, method-of-line approach, and others are not applied; (ii) the time stability analysis is not discussed; and (iii) recomputation of the resulting matrix at each time level as done for other methods for solving partial differential equations (PDEs) with variable coefficients is avoided and the matrix is computed once. …”
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Effect of Intervention of Vaccination and Treatment on the Transmission Dynamics of HBV Disease: A Mathematical Model Analysis by Firaol Asfaw Wodajo, Temesgen Tibebu Mekonnen

“…The model is studied qualitatively using the stability theory of differential equations and the effective reproductive number which represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. …”
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The levelized cost of energy in the presence of uncertainty on the offshore wind speed by J. Pablo Arenas-López, Mohamed Badaoui

“…To carry out this task, we employ two techniques based on stochastic differential equations to generate wind power scenarios. Utilizing 40 years of recorded wind speed data sourced from the MERRA-2 reanalysis, we derive the input parameters of the models from fitting to 4-parameter Dagum and Johnson SB probability distributions, which shows that accurate modeling of offshore wind speeds requires dealing with complex mathematical functions that need numerical computation. …”
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New super and shock like solitary structures for KdV equation with higher-order nonlinearity by H.S. Alayachi, Abdulghani Alharbi, E.K. El-Shewy, Mahmoud A.E. Abdelrahman

“…The modified F-expansion approach is an effective, powerful and straightforward method for obtaining the solitary wave solutions to the nonlinear partial differential equations (NPDEs). The effect of model parameters on the nature, properties and structures of the model solutions have been examined. …”
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Motion Control of a 4WS4WD Path-Following Vehicle: Dynamics-Based Steering and Driving Models by Zhonghua Zhang, Caijin Yang, Weihua Zhang, Yanhai Xu, Yiqiang Peng, Maoru Chi

“…The vehicle path-following dynamics are modeled using the classical mass-damper-spring vibration theory, which is described by three ordinary differential equations of second order with lateral, heading and velocity deviations, and control parameters. …”
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Positive Solutions Depending on Parameters for a Nonlinear Fractional System with p-Laplacian Operators by Chen Yang, Xiaolin Zhu

“…This paper considers a system of fractional differential equations involving p-Laplacian operators and two parameters D0+α1φp1D0+β1ut+λft,ut,vt=0,0<t<1,D0+α2φp2D0+β2vt+μgt,ut,vt=0,0<t<1,u0=u1=u′0=u′1=0,D0+β1u0=0,D0+β1u1=b1D0+β1uη1,v0=v1=v′0=v′1=0,D0+β2v0=0,D0+β2v1=b2D0+β2vη2, where αi∈1,2, βi∈3,4, D0+αi and D0+βi are the standard Riemann-Liouville derivatives, φpis=spi−2s,pi>1, φpi−1=φqi, 1/pi+1/qi=1,ηi∈0,1,bi∈0,ηi1−αi/pi−1, i=1,2, and f,g∈C0,1×0,+∞×0,+∞,0,+∞ and λ and μ are two positive parameters. …”
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Bifurcation and controller design in a 3D delayed predator-prey model by Jinting Lin, Changjin Xu, Yiya Xu, Yingyan Zhao, Yicheng Pang, Zixin Liu, Jianwei Shen

“…This paper determines the parameter conditions for system stability and the occurrence of bifurcations by employing bifurcation theory and the stability theory of delayed differential equations. Using two control strategies, namely the mixed controller and the extended delay feedback controller, this paper effectively adjusts the stability domain of the delayed predator-prey systems and controls the time of bifurcation onset. …”
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Exploring the implications of ternary Jeffrey nanofluid on pulsating flow and heat transfer through unsymmetrical corrugated micro conduit by Mohamed S. Abdel-wahed, Khaled S. Mekheimer, Ahmed Y. Sayed, Shaaban I. Ahmed

“…Using the perturbation method and Mathematica software, we derived semi-analytical solutions for the governing partial differential equations in their complex form. nanoparticle-enhanced blood exhibits improved thermal performance compared to pure fluid, with the type and concentration of nanoparticles (Fe3O4, Au, SWCNTs) significantly impacting heat dissipation and temperature distribution within the microfluidic conduit. …”
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FEATURES OF ELECTROMECHANICAL ACOUSTIC ENERGY CONVERSION BY CYLINDRICAL PIEZOCERAMIC TRANSDUCERS WITH INTERNAL SCREENS IN COMPOSITION OF FLAT SYSTEMS by A. G. Leiko, I. V. Kandrachuk, A. O. Sviatnenko

“…The physical fields arising from the emission of sound by such a system are determined by the joint solution of the system of differential equations: the wave equation; equations of motion of thin piezoceramic shells with circular polarization in displacements; the equations of forced electrostatics for piezoceramics at given boundary conditions, the conditions of conjugation of fields at the boundaries of the division of domains and electric conditions.The solution of the problem is reduced to the solution of an infinite system of linear algebraic equations with respect to unknown coefficients of field expansions.An analysis of the results of numerical calculations, performed on the basis of the obtained analytical relations, called to establish a number of features in the electromechanical acoustic transformation of energy by emitters in the composition of flat systems. …”
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A Multibody Model of Tilt-Rotor Aircraft Based on Kane’s Method by Jianmin Su, Chengyue Su, Sheng Xu, Xiaoxing Yang

“…The generalized active forces and generalized inertial forces of both the body and the nacelles (with rotors) are obtained, respectively, and the first-order differential equations of the generalized rates are obtained. …”
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Jeffrey fluid flow past inclined stretchable sheet with magnetic dipole and suction/injection by Iyoko M.O., Olajuwon B.I., Fagbemiro O., Raji M.T.

“…The applicable equations were changed into nonlinear ordinary differential equations by similarity transformations. With the Chebyshev spectral collocation approach, solutions were obtained for fluid velocity and temperature. …”
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