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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Measuring the Pollutants in a System of Three Interconnecting Lakes by the Semianalytical Method by Indranil Ghosh, M. S. H. Chowdhury, Suazlan Mt Aznam, M. M. Rashid

“…The lake pollution model is formulated into the three-dimensional system of differential equations with three instances of input. In the present study, the new iterative method (NIM) was applied to the lake pollution model with three cases called impulse input, step input, and sinusoidal input for a longer time span. …”
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Stagnation Point Flow of Nanofluid over a Moving Plate with Convective Boundary Condition and Magnetohydrodynamics by Fazle Mabood, Nopparat Pochai, Stanford Shateyi

“…The governing partial differential equations for the fluid flow, temperature, and concentration are reduced to a system of nonlinear ordinary differential equations. …”
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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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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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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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An Approximate Solution for a Class of Ill-Posed Nonhomogeneous Cauchy Problems by Nihed Teniou, Salah Djezzar

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Variational Approach to Impulsive Problems: A Survey of Recent Results by Fang-fang Liao, Juntao Sun

“…We present a survey on the existence of nontrivial solutions to impulsive differential equations by using variational methods, including solutions to boundary value problems, periodic solutions, and homoclinic solutions.…”
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An Lp-Estimate for Weak Solutions of Elliptic Equations by Sara Monsurrò, Maria Transirico

“…We prove an Lp-a priori bound, p>2, for solutions of second order linear elliptic partial differential equations in divergence form with discontinuous coefficients in unbounded domains.…”
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S-asymptotic expansion of distributions by Bogoljub Stankovic

“…This paper contains first a definition of the asymptotic expansion at infinity of distributions belonging to G′Rn, named S-asymptotic expansion, as also its properties and application to partial differential equations.…”
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Uniqueness and Existence of Solution for a System of Fractional q-Difference Equations by Wen-Xue Zhou, Hai-zhong Liu

“…We prove the existence and uniqueness of solution for a system of fractional differential equations. Our results are based on the nonlinear alternative of Leray-Schauder type and Banach’s fixed-point theorem.…”
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A min-max theorem and its applications to nonconservative systems by Li Weiguo, Li Hongjie

“…And it is used to prove a new existence results for a nonconservative systems of ordinary differential equations with resonance.…”
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Optimal Portfolio Selection of Mean-Variance Utility with Stochastic Interest Rate by Shuang Li, Shican Liu, Yanli Zhou, Yonghong Wu, Xiangyu Ge

“…By solving the corresponding nonlinear partial differential equations (PDEs) deduced from the extended HJB equation, the analytical solutions of the optimal investment strategies under time inconsistency are derived. …”
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Sliding Mode Output Feedback Control of a Flexible Rotor Supported by Magnetic Bearings by A. S. Lewis, A. Sinha, K. W. Wang

“…A mathematical model of the rotor]magnetic bearing system is presented in terms of partial differential equations. These equations are then discretized into a finite number of ordinary differential equations through Galerkin’s method. …”
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Nonlinear Parametric Vibration and Chaotic Behaviors of an Axially Accelerating Moving Membrane by Mingyue Shao, Jimei Wu, Yan Wang, Qiumin Wu

“…The Galerkin method is employed for discretizing the vibration partial differential equations. However, the solutions concerning to differential equations are determined through the 4th order Runge–Kutta technique. …”
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SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects by Tongqian Zhang, Xinzhu Meng, Tonghua Zhang

“…We first propose a new epidemic disease model governed by system of impulsive delay differential equations. Then, based on theories for impulsive delay differential equations, we skillfully solve the difficulty in analyzing the global dynamical behavior of the model with pulse vaccination and impulsive population input effects at two different periodic moments. …”
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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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Hopf bifurcation on one of tumor models by Algis Kavaliauskas

“…The model is described by the system of second order differential equations. The region of parameters is determined where the Hopf bifurcation of the stationary zero point is possible. …”
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