Study of Heat Transfer under the Impact of Thermal Radiation, Ramped Velocity, and Ramped Temperature on the MHD Oldroyd-B Fluid Subject to Noninteger Differentiable Operators by Syed Tauseef Saeed, Ilyas Khan, Muhammad Bilal Riaz, Syed Muhammad Husnine

“…The mathematical analysis of fractional governing partial differential equations has been established using systematic and powerful techniques of Laplace transform with its numerical inversion algorithms. …”
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Inference of a three-gene network underpinning epidermal stem cell development in Caenorhabditis elegans by Alicja Brożek, Arianna Ceccarelli, Andreas Christ Sølvsten Jørgensen, Mark Hintze, Vahid Shahrezaei, Michalis Barkoulas

“…We validate its significance at the L1 stage with ordinary differential equations and Bayesian modeling, making testable predictions for a double mutant. …”
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Artificial neural networks for stability analysis and simulation of delayed rabies spread models by Ramsha Shafqat, Ateq Alsaadi

“…This study addressed the complexity of rabies spread by integrating two critical delay effects—vaccination efficacy and incubation duration—into a delay differential equations model, capturing more realistic infection patterns between dogs and humans. …”
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Characterization of the dynamic behavior of nonlinear biosystems in the presence of model uncertainty using singular invariance PDEs: Application to immobilized enzyme and... by Nikolaos Kazantzis, Vasiliki Kazantzi

“…The problem of interest is addressed within the context of singular partial differential equations (PDE) theory, and in particular, through a system of singular quasi-linear invariance PDEs for which a general set of conditions for solvability is provided. …”
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Study of COVID-19 cases with real data analysis by Wedad Albalawi, Kottakkaran Sooppy Nisar, Nadir Omer, Adnan Aslam, Takasar Hussain, Muhammad Ozair, Shahid Hussain, Nida Hameed

“…In this work, patients of corona virus disease 2019, known as COVID-19, have been studied in Pakistan and its neighboring countries Iran, India and Afghanistan through the mathematical model in the form of coupled system of five ordinary differential equations. Two types of equilibria, infection free and endemic, are obtained. …”
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Two-loop planar master integrals for NNLO QCD corrections to W-pair production in quark-antiquark annihilation by Wen-Jie He, Ren-You Zhang, Liang Han, Yi Jiang, Zhe Li, Xiao-Feng Wang, Shu-Xiang Li, Pan-Feng Li, Qing-hai Wang

“…These MIs are analytically calculated using the method of differential equations, with solutions expanded as Taylor series in the dimensional regulator ϵ. …”
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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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Exact solutions for the Cahn–Hilliard equation in terms of Weierstrass-elliptic and Jacobi-elliptic functions by Akhtar Hussain, Tarek F. Ibrahim, F. M. Osman Birkea, Abeer M. Alotaibi, Bushra R. Al-Sinan, Herbert Mukalazi

“…Abstract Despite the historical position of the F-expansion method as a method for acquiring exact solutions to nonlinear partial differential equations (PDEs), this study highlights its superiority over alternative auxiliary equation methods. …”
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Influence of titanium and gold platelet morphology on heat transfer in biomagnetic third-grade hybrid nanofluid flow through a vertical channel by S. Suneetha, S.R.R. Reddy, Maduru Lakshmi Rupa, T. Mahesh Kumar, Mohammed Jameel, Taoufik Saidani, Lamia Abu El Maati, Dilsora Abduvalieva, M. Ijaz Khan

“…Through the use of perturbation, the nonlinear momentum and energy equations are reduced to nonlinear ordinary differential equations. The collocation method is utilized to solve these transformed equations. …”
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Analytical Solutions of Fractional Walter’s B Fluid with Applications by Qasem Al-Mdallal, Kashif Ali Abro, Ilyas Khan

“…By employing the dimensional analysis, the dimensional governing partial differential equations have been transformed into dimensionless form. …”
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Bat population dynamics: multilevel model based on individuals' energetics by Paula Federico, Dobromir T. Dimitrov, Gary F. McCracken

“…A structured population model based on extended McKendrick-von Foerster partial differential equations integrates those individual dynamics and provides insight into possible regulatory mechanisms of population size as well as conditions of population survival and extinction. …”
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ON THE TECHNIQUE OF MODELING ONTOGENETIC CHANGES IN FISH AND INSECTS LIFECYCLE by A. Yu. Perevaryukha

“…The method has been for submission to decline of generations on the basis of dynamic overriding differential equations with discrete-continuous structure of time. …”
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A Nonoscillatory Second-Order Time-Stepping Procedure for Reaction-Diffusion Equations by Philku Lee, George V. Popescu, Seongjai Kim

“…After a theory of morphogenesis in chemical cells was introduced in the 1950s, much attention had been devoted to the numerical solution of reaction-diffusion (RD) partial differential equations (PDEs). The Crank–Nicolson (CN) method has been a common second-order time-stepping procedure. …”
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EVOLUTION OF THE ROTATIONAL MOTION OF A SATELLITE WITH FLEXIBLE VISCOELASTIC RODS ON THE ELLIPTIC ORBIT by E. V. Sadovnikova, A. V. Shatina

“…We obtain an averaged system of differential equations in the Andoyer variables, which describes the evolution of the satellite's rotational motion. …”
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Analysis of Model Parameters for a Polymer Filtration Simulator by N. Brackett-Rozinsky, S. Mondal, K. R. Fowler, E. W. Jenkins

“…The simulator is a three-dimensional, time-dependent discretization of a coupled system of nonlinear partial differential equations used to model fluid flow and debris transport, along with statistical relationships that define debris distributions and retention probabilities. …”
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Synchronization of Two Self-Synchronous Vibrating Machines on an Isolation Frame by Chunyu Zhao, Qinghua Zhao, Zhaomin Gong, Bangchun Wen

“…Using the modified average method of small parameters, we deduce the non-dimensional coupling differential equations of the disturbance parameters for the angular velocities of the four unbalanced rotors. …”
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Theoretical investigation on models of circadian rhythms based on dimerization and proteolysis of PER and TIM by Jifa Jiang, Qiang Liu, Lei Niu

“…By imposing assumptions that the dimerization reactions were fast and dimeric proteins were in rapid equilibrium, they reduced the model to a pair of nonlinear ordinary differential equations of mRNA and total protein concentrations. …”
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Nonlinear Dynamics Analysis of the Wind Turbine Gear Transmission System Considering Friction Effect by Xu Fan, Liu Wenbin, Zhang Haibo, Zhang Qiang, Wu Shijing, Wang Xiaosun, Duan Jiujun

“…After nondimensionalization, the dynamics differential equations are obtained. Runge-Kutta methods are adopted to solve equations and the nonlinear dynamic response of the wind turbine gear transmission system is acquired. …”
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A Mathematical and Numerically Integrable Modeling of 3D Object Grasping under Rolling Contacts between Smooth Surfaces by Suguru Arimoto, Morio Yoshida

“…A set of 1st-order differential equations governing rotational motions of each fingertip and the object and updating arc-length parameters should be accompanied with the Euler-Lagrange equations. …”
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Mathematical Modeling of Coccidiosis Dynamics in Chickens with Some Control Strategies by Yustina A. Liana, Mary C. Swai

“…Using the theory of differential equations, the invariant set of the model was derived, and the model’s solution was found to be mathematically and biologically significant. …”
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