Exact Solutions for Unsteady Free Convection Flow of Casson Fluid over an Oscillating Vertical Plate with Constant Wall Temperature by Asma Khalid, Ilyas Khan, Sharidan Shafie

“…The governing partial differential equations corresponding to the momentum and energy equations are transformed into linear ordinary differential equations by using nondimensional variables. …”
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Stability and Bifurcation for a Delayed Diffusive Two-Zooplankton One-Phytoplankton Model with Two Different Functions by Xin-You Meng, Li Xiao

“…Furthermore, due to the local bifurcation theory of partial functional differential equations, Hopf bifurcation of the model is investigated by considering time delay as the bifurcation parameter. …”
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An Exact Solution of the Binary Singular Problem by Baiqing Sun, Kun Tang, Hongmei Zhang, Shan Xiong

“…Such ordinary differential equations accompany singular coefficients. In this paper, by using the properties of reproducing kernel, the exact solution expressions of dual singular problem are given in the reproducing kernel space and studied, also for a class of singular problem. …”
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Self-organization through decoupling by Romar Correa

“…On the other hand, we provide a theorem showing that a coupled set of differential equations can become uncoupled and vice versa as an argument in favour of the second thesis. …”
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Classification of the Group Invariant Solutions for Contaminant Transport in Saturated Soils under Radial Uniform Water Flows by M. M. Potsane, R. J. Moitsheki

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Stability Analysis of an Alcoholism Model with Public Health Education and NSFD Scheme by Zhaofeng An, Suxia Zhang, Jinhu Xu

“…In this paper, an alcoholism model of SEAR type with different susceptibilities due to public health education is investigated, with the form of continuous differential equations as well as discrete differential equations by applying the Mickens nonstandard finite difference (NSFD) scheme to the continuous equations. …”
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Travelling wave solutions to some PDEs of mathematical physics by Kourosh Nozari, Ghasem Alizadeh Afrouzi

“…As a result, some ambiguities arise when we want to solve nonlinear partial differential equations such as differential equations of elasticity and multifluid flows, or some new cosmological models such as signature changing space-times. …”
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Influence of Center Component Floating on the Load-sharing Characteristic of Planetary Transmission System by Yangyang Du, Xiaosun Wang, Xue Yang, Bo Jiao, Shijing Wu

“…By solving the differential equations， the influences of the support stiffness of the center component and the clearance floating on the load-sharing performance of the planetary gear train are analyzed. …”
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Convergence Analysis Hilbert Space Approach for Fuzzy Integro-Differential Models by Jingwen Zhang

“…The first application of a technique for solving Volterra integro-differential equations of the fuzzy type, which was devised and tested in this paper, is shown here. …”
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Some Nonlinear Fractional PDEs Involving β-Derivative by Using Rational exp−Ωη-Expansion Method by Haifa Bin Jebreen

“…Some fractional PDEs will convert to consider ordinary differential equations (ODEs) with the help of transformation β-derivative. …”
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Flow over Exponentially Stretching Sheet through Porous Medium with Heat Source/Sink by I. Swain, S. R. Mishra, H. B. Pattanayak

“…The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and then solved numerically using a fourth-order Runge-Kutta method with a shooting technique. …”
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Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems by Mohamed Hannabou, Khalid Hilal, Ahmed Kajouni

“…In this paper, a class of nonlocal impulsive differential equation with conformable fractional derivative is studied. …”
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Lie Group Analysis of Unsteady Flow and Heat Transfer over a Porous Surface for a Viscous Fluid by M. B. Akgül, G. Sarı, M. Pakdemirli

“…Adopting the obtained symmetry groups, governing partial differential equations are converted into ordinary differential equations and then solved numerically. …”
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Unsteady MHD Mixed Convection Flow of Chemically Reacting Micropolar Fluid between Porous Parallel Plates with Soret and Dufour Effects by Odelu Ojjela, N. Naresh Kumar

“…A suitable similarity transformation is used to reduce the governing partial differential equations into nonlinear ordinary differential equations and then solved numerically by the quasilinearization method. …”
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Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis by N. Mindu, D. P. Mason

“…The migration of melt through the mantle of the Earth is governed by a third-order nonlinear partial differential equation for the voidage or volume fraction of melt. …”
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Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps by Tingting Ma, Xinzhu Meng, Zhengbo Chang

“…Using the comparison theorem of stochastic differential equations and asymptotic approaches, sufficient conditions for persistence in mean and extinction of three species are derived. …”
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Lie Symmetry Analysis for the General Classes of Generalized Modified Kuramoto-Sivashinsky Equation by Rong Qi, Muhammad Mobeen Munir, Nazish Younas, Muhammad Idrees, Jia-Bao Liu

“…Lie symmetry analysis of differential equations proves to be a powerful tool to solve or at least reduce the order and nonlinearity of the equation. …”
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An Approximate Solution for a Class of Ill-Posed Nonhomogeneous Cauchy Problems by Nihed Teniou, Salah Djezzar

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A simplified version of the method of calculation of multilayer composite rods according to the theory of A.R. Rzhanitsyn by V. V. Filatov, Thi Linh Quyen Hoang

“…This assumption allows us to reduce the problem of determining the functions of shear forces to solving one ordinary differential equation of the second order. Thus, the number of simultaneously solved differential equations describing the problem is reduced from n + 2 to three for any number of layers.Materials and methods. …”
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Chemical reaction and Soret impacts on MHD heat and mass transfer Casson hybrid nanofluid (MoS2+ZnO) flow based on engine oil across a stretching sheet with radiation by M. Radhika, Y. Dharmendar Reddy

“…The relevant similarity variables convert the governing nonlinear partial differential equations to ordinary differential equations (ODEs). …”
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