An Efficient Approach for Fractional Harry Dym Equation by Using Sumudu Transform by Devendra Kumar, Jagdev Singh, A. Kılıçman

“…The results obtained by the two methods are in agreement, and, hence, this technique may be considered an alternative and efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations. The HPSTM is a combined form of sumudu transform, homotopy perturbation method, and He’s polynomials. …”
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Existence Analysis of Multi-Point Boundary Value Problems with Riesz-Caputo Fractional Derivatives by Takieddine Zeghida, Rabah Khaldi, Assia Guezane-Lakoud

“…This paper explores the study of a specific category of nonlinear multi-point boundary value problems (BVPs) associated with Riesz-Caputo fractional differential equations and integral boundary conditions. The primary objective is to establish the existence of solutions under specific assumptions. …”
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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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Computing the Electric and Magnetic Matrix Green’s Functions in a Rectangular Parallelepiped with a Perfect Conducting Boundary by V. G. Yakhno, Ş. Ersoy

“…This method is based on approximation (regularization) of the Dirac delta function and its derivatives, which appear in the differential equations for magnetic and electric Green’s functions, and the Fourier series expansion meta-approach for solving the elliptic boundary value problems. …”
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Binary mixture convection in a horizontal channel under the Soret effect action by Stepanova Irina

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SIMULATION OF OPEN MECHANISMS FOR THE ADDITIVE PROCESS WELD PLASTICS by N. N. Hurski, V. A. Skachek, A. V. Skachek, Y. A. Skudnyakov

“…This article discusses: model of the two-link mechanism; generalized scheme of mechatronic simulation model of 3D-printer with the positioning units of electric DC; mathematical model of the actuator of the printer unit in the form of a system of differential equations; 3D-printer programming model implemented in the Matlab-Simulink environment using the c standard library blocks and SimMechanics library; virtual (animated) 3D printer model on the basis of the library Simulink 3D Animation, supports the visualization of the movements of the designed mechanism of the basic units. …”
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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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A Mathematical Model For The Population Dynamics Of Disease Transmiting Vectors in Particular Female Anopheles Mosquitoes. by Turyamusiima, Richard

“…The mosquito free equilibrium and endemic equilibrium have been determined by setting system of ordinary differential equations to zero. Basic reproduction has been determined using the next generation matrix management analyzed. …”
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A multi-layer neural network-based evaluation of MHD radiative heat transfer in Eyring–Powell fluid model by Muflih Alhazmi, Zahoor Shah, Muhammad Asif Zahoor Raja, Nafisa A. Albasheir, Maryam Jawaid

“…To facilitate analysis, governing partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) only with the aid of similarity transformations. …”
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Modeling of the migration of endothelial cells on bioactive micropatterned polymers by Thierry Colin, Marie-Christine Durrieu, Julie Joie, Yifeng Lei, Youcef Mammeri, Clair Poignard, Olivier Saut

“…It isbased on a system of partial differential equations ofPatlak-Keller-Segel type that describes theevolution of the cell densities. …”
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Control Application of Piezoelectric Materials to Aeroelastic Self-Excited Vibrations by Mohammad Amin Rashidifar, Darvish Ahmadi

“…The governing differential equations of an overhung beam are established. …”
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A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems by S. S. Motsa

“…The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. …”
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A One-Point Third-Derivative Hybrid Multistep Technique for Solving Second-Order Oscillatory and Periodic Problems by Mufutau Ajani Rufai, Ali Shokri, Ezekiel Olaoluwa Omole

“…This paper describes a third-derivative hybrid multistep technique (TDHMT) for solving second-order initial-value problems (IVPs) with oscillatory and periodic problems in ordinary differential equations (ODEs), the coefficients of which are independent of the frequency omega and step size h. …”
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Research of the Influence of Tooth Surface Wear and Bearing Clearance on Gear Dynamics by Kaida Wang, Ruiliang Zhang, Tie Wang, Yatian Zhou, Fei Wang

“…Tooth surface wear and bearing clearance are important factors affecting gear system dynamics, in order to reveal the influence of tooth wears and bearing clearance on the dynamics of gear system, a six-degree-of-freedom bending-torsion coupled model is established, which takes into account the tooth surface wear, bearing clearance, friction and backlash. The dynamic differential equations are solved by Runge-Kutta method and the dynamic response of the system is obtained. …”
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Strength Analysis for Cage of Planetary Wheel Needle Roller Bearing by Yubo Wang, Haisheng Yang, Manjun Xu, Yongcun Cui, Sier Deng

“…Aiming to solving the problem of cage failure under revolution-rotation，based on the dynamics theory of rolling bearing，the dynamics differential equations of needle roller bearing coupled with revolution-rotation working condition are established，and GSTIFF variable step length integral algorithm is adopted to solve the bearing. …”
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Peridynamic Formulation for Coupled Thermoelectric Phenomena by Migbar Assefa, Xin Lai, Lisheng Liu, Yang Liao

“…This is because traditional methods are developed based on partial differential equations (PDEs) and lead to infinite fluxes at the discontinuities. …”
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Effects of Thermal Radiation on Mixed Convection Flow of a Micropolar Fluid from an Unsteady Stretching Surface with Viscous Dissipation and Heat Generation/Absorption by Khilap Singh, Manoj Kumar

“…The model contains nonlinear coupled partial differential equations which have been converted into ordinary differential equation by using the similarity transformations. …”
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Some Properties of Solutions to Multiterm Fractional Boundary Value Problems with p-Laplacian Operator by KumSong Jong, HuiChol Choi, KyongJun Jang, SongGuk Jong, KyongSon Jon, Ok Ri

“…In this paper, we study some properties of positive solutions to a class of multipoint boundary value problems for nonlinear multiterm fractional differential equations with p-Laplacian operator. Using the Banach contraction mapping principle, the existence, the uniqueness, the positivity, and the continuous dependency on m-point boundary conditions of the solutions to the given problem are investigated. …”
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Finite element approximation of a population spatial adaptation model by Gonzalo Galiano, Julián Velasco

“…In [18], Sighesada, Kawasaki and Teramoto presented a system of partial differential equations for modeling spatial segregation of interacting species. …”
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Robust H∞ Control for a Class of Nonlinear Distributed Parameter Systems via Proportional-Spatial Derivative Control Approach by Cheng-Dong Yang, Jianlong Qiu, Jun-Wei Wang

“…This paper addresses the problem of robust H∞ control design via the proportional-spatial derivative (P-sD) control approach for a class of nonlinear distributed parameter systems modeled by semilinear parabolic partial differential equations (PDEs). By using the Lyapunov direct method and the technique of integration by parts, a simple linear matrix inequality (LMI) based design method of the robust H∞ P-sD controller is developed such that the closed-loop PDE system is exponentially stable with a given decay rate and a prescribed H∞ performance of disturbance attenuation. …”
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