A Hybrid Power Series Artificial Bee Colony Algorithm to Obtain a Solution for Buckling of Multiwall Carbon Nanotube Cantilevers Near Small Layers of Graphite Sheets by Aminreza Noghrehabadi, Mohammad Ghalambaz, Mehdi Ghalambaz, Afshin Ghanbarzadeh

“…A trial solution of the differential equation is defined as sum of two polynomial parts. …”
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Mathematical insights on psoriasis regulation: Role of Th1 and Th2 cells by Amit Kumar Roy, Priti Kumar Roy, Ellina Grigorieva

“…In this article, we have constructed a set of nonlinear differential equations involving the above cell population for better understanding the impact of cytokines on Psoriasis. …”
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Nonlinear Autoregressive Neural Network for Antimicrobial Waste Water Treatment by Anwer Mustafa Hilal, Mashael M. Asiri, Shaha Al-Otaibi, Faisal Mohammed Nafie, Amal Al-Rasheed, Mohammed Rizwanullah, Ishfaq Yaseen, Abdelwahed Motwakel

“…Dirichlet design parameters and a combined combination of Neumann and Dirichlet boundary situation are applied to the system of differential equations. In addition, the proposed method use the learning under supervision technique of a nonlinear autoregressive for estimating the CO2 concentration and flows in units of rate of a reaction characteristics, an exogenous (NARX) neural network model with two activation functions was used (Log-sigmoid and hyperbolic tangent) and for both the findings of a TC and SMX absorption simulations showed the random forest performed support vector tree and nonlinear autoregressive exogenous neural networks and machine learning methods. …”
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Differential game theory application in models of trade relations of Great Britain with Portugal and Russia with Belarus by I. V. Korolyov

“…The author composes and analyzes a system of four nonlinear ordinary differential equations with parameters, and their (dynamic) variation leads to the improvement of successive approximations of the exact solution, the finding of which is very problematic. …”
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Data-driven model discovery and model selection for noisy biological systems. by Xiaojun Wu, MeiLu McDermott, Adam L MacLean

“…Biological systems exhibit complex dynamics that differential equations can often adeptly represent. Ordinary differential equation models are widespread; until recently their construction has required extensive prior knowledge of the system. …”
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Asymptotical Behavior of the Solution of a SDOF Linear Fractionally Damped Vibration System by Z.H. Wang, M. L. Du

“…The solutions of the initial value problems of linear fractional differential equations are usually expressed in terms of Mittag-Leffler functions or some other kind of power series. …”
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Study on construction and identification of dynamic model of precooler in aviation bleed air system by SHI Zhouzheng, DONG Minghao, LIU Qi, LUO Ziyan, WANG Hongbo, QIN Xiansheng, WANG Zhanxi

“…The finite element method was used to establish the partial differential equation of the heat exchange mechanism, and the heat exchange mechanism of the precooler was analyzed. …”
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Control optimization of air traffic emissions in a two-variable dynamic model by F. A. Buendía-Hernández, M. J. OrtizBevia, F. J. Alvarez-Garcia, A. RuizdeElvira, J. M. Salazar

“…This study used a two variable differential equations model with a non-linear control term to address several aspects of the emissions stabilization issue. …”
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Robust pareto multiobjective optimum design of FG-Beam under moving mass by Moein Abdollah-Salimi, Nader Nariman-Zadeh, Reza Ansari

“…By substituting terms of energy into the Lagrange equation, differential equations of motion are obtained. Displacement fields as a function of time and x-coordinate are calculated by means of the numerical solution of the above-mentioned equations. …”
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Investigation of properties of system of automatic control of liquid-propellant rocket propulsion system with integrating regulator by I. A. Kyzmenko, A. B. Yakovlev

“…There are obtained differential equations describing the operation of the comparison element, the throttle valve, the hydraulic amplifier, and the processes in the gas generator. …”
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Global stability for a mosquito-borne disease model with continuous-time age structure in the susceptible and relapsed host classes by Maria Guadalupe Vazquez-Peña, Cruz Vargas-De-León, Jorge Velázquez-Castro

“…The system of integro-differential equations uses flexible, unspecified functions to represent these dependencies, assuming they are integrable. …”
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Steady Three-Dimensional MHD Mixed Convection Couple Stress Flow of Hybrid Nanofluid with Hall and Ion Slip Effect by Ali Rehman, Waris Khan, Ebenezer Bonyah, Samsul Ariffin Abdul Karim, Ahmed Alshehri, Ahmed M. Galal

“…To transform the nonlinear partial differential equation to a nonlinear ordinary differential equation we used the defined similarity transformation. …”
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On the possibility of controlling the temperature of gases and liquids in a transportation system by local cooling or heating with account salt deposition by Evgeny L. Pankratov

“…The model is based on an analytical solution of partial differential equations with nonlinearity and variation of their coefficients in space and time. …”
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Simple Ion Transfer at Liquid|Liquid Interfaces by L. J. Sanchez Vallejo, J. M. Ovejero, R. A. Fernández, S. A. Dassie

“…We describe numerical simulations implementing different approaches for solving the differential equations associated with the mass transport and charge transfer. …”
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Artificial neural network analysis of Jeffrey hybrid nanofluid with gyrotactic microorganisms for optimizing solar thermal collector efficiency by Anup Kumar, Bhupendra K. Sharma, Bandar Almohsen, Laura M. Pérez, Kamil Urbanowicz

“…The non-similar variables are introduced to the dimensional governing equations to get the non-dimensional ordinary differential equations. The Cash and Carp method is implemented to solve the non-dimensional equations. …”
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Mathematical analysis of Lassa fever epidemic with real data by Adnan Aslam, Takasar Hussain, Muhammad Ozair, Arfah Hafeez, Wedad Albalawi, Mohammed Zakarya, Nadir Omer

“…Seven dimensional mathematical model is considered as the system of ordinary differential equations. First, we compute the equilibrium point in which no disease exists then, after finding the reproduction number, both types of stabilities, local and global, of this equilibrium point is discussed. …”
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Effect of Tooth Surface Friction on Bending Torsional Axial Pendular Coupling Nonlinear Amplitude Frequency Characteristic of Marine Herringbone Gear by Haoqin Zhang, Hao Dong, Libang Wang, Xiaolong Zhao

“…The Runge-Kutta numerical method is used to solve the differential equation. The phase diagram and time history diagram of the non-dimensional frequency system under the influence of tooth surface friction are obtained. …”
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What can mathematical models tell us about the relationship between circular migrations and HIV transmission dynamics? by Aditya S. Khanna, Dobromir T. Dimitrov, Steven M. Goodreau

“…We construct models from each class, usingordinary differential equations and exponential random graph models,respectively. …”
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Radionuclide Transport in Fractured Rock: Numerical Assessment for High Level Waste Repository by Claudia Siqueira da Silveira, Antonio Carlos Marques Alvim, Jose de Jesus Rivero Oliva

“…Transport in the fracture is assumed to obey an advection-diffusion equation, while molecular diffusion is considered the dominant mechanism of transport in porous matrix. The partial differential equations describing the movement of radionuclides were discretized by finite difference methods, namely, fully explicit, fully implicit, and Crank-Nicolson schemes. …”
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Hydromagnetic Flow of Two Immiscible Couple Stress Fluids through Porous Medium in a Cylindrical Pipe with Slip Effect by Punnamchandar Bitla, Yitagesu Daba Kore

“…The resulting differential equations governing the flow in the two regions are converted to nondimensional forms using appropriate dimensionless variables. …”
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