A Note on the Fractional Generalized Higher Order KdV Equation by Yongyi Gu

“…It has showed that the applied method is very useful and is practically well suited for the nonlinear differential equations, those arising in mathematical physics.…”
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Mathematical modeling of the military operation by Albertas Pincevičius, Rimantas-Jonas Rakauskas, Gintautas Misevičius

“… The aim of this paper is show how the systems of differential equations may be applied both to describe the battle actions between the regular army and the partisans. …”
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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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Global attractivity without stability for Liénard type systems by Marian Mureşan

“…We are concerned with some conditions such as the trivial solution of a planar system of differential equations (including the Liénard system) that is globally attractive but not stable. …”
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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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Oscillation Theorems for Even Order Damped Equations with Distributed Deviating Arguments by Chunxia Gao, Peiguang Wang

“…A class of even order damped differential equations with distributed deviating arguments are investigated. …”
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Some Generalized Gronwall-Bellman Type Impulsive Integral Inequalities and Their Applications by Yuzhen Mi

“…Our result is also applied to study a boundary value problem of differential equations with impulsive terms.…”
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MHD Williamson Nanofluid Flow over a Stretching Sheet through a Porous Medium under Effects of Joule Heating, Nonlinear Thermal Radiation, Heat Generation/Absorption, and Chemical... by J. Bouslimi, M. Omri, R. A. Mohamed, K. H. Mahmoud, S. M. Abo-Dahab, M. S. Soliman

“…The system of nonlinear partial differential equations governing the study of fluid flow has transformed into a system of ordinary differential equations using similarity transformations and nondimensional variables which were subsequently solved numerically by using the Rung-Kutta fourth-order method with shooting technique. …”
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Analytical study of steady state axisymmetric stagnation-point gold–blood Casson nanofluid through a rotating stretchable disk by Usman Ali, Hamid Khan, Waris Khan, Emad E. Mahmoud, Marouan Kouki, Jabr Aljedani, Hakim AL Garalleh

“…By using scaling variables, the complex system of partial differential equations is simplified into a set of coupled high degree nonlinear ordinary differential equations with convective boundary conditions. …”
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Computational analysis of bioconvective MHD hybrid nanofluid flow of non-Newtonian fluid over cone/plate: A study based on the Cattaneo-Christov heat and mass flux model by P. Francis, P. Sambath, S. Noeiaghdam, U. Fernandez-Gamiz, S. Dinarvand

“…A similarity transformation is used to simplify the complex partial differential equations into ordinary differential equations, which are then solved using the Keller Box finite difference method. …”
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Heat transport efficiency in rheology of radiated casson material due to porous shrinking cylinder by Muhammad Yasir, N. Ameer Ahammad, Aisha M. Alqahtani, Yahia Said

“…The physical characteristics of the problem are governed by partial differential equations, which are converted to ordinary differential equations using appropriate similarity variables. …”
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Lie-symmetry analysis of a three dimensional flow due to unsteady stretching of a flat surface with non-uniform temperature distribution by Ghani Khan, Muhammad Safdar, Safia Taj, Adnan Munir, Muhammad Tauseef Nasir

“…Twelve Lie point symmetries for the nonlinear partial differential equations describing the considered flow and heat transfer phenomena are derived. …”
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Predicting Tipping Points in a Family of PWL Systems: Detecting Multistability via Linear Operators Properties by Joaquin Alvarez-gallegos, Sishu Shankar Muni, Hector Gilardi-velázquez, Rıcardo Cuesta-garcía, J. L. Echenausía-monroy

“…The study of dynamical systems is based on the solution of differential equations that may exhibit various behaviors, such as fixed points, limit cycles, periodic, quasi-periodic attractors, chaotic behavior, and coexistence of attractors, to name a few. …”
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An EPQ inventory model with Weibull distribution, dynamic time-dependent holding cost under various demand pattern using Maclaurin series approximations by Gopal Kumar Gupta, Atma Nand, N. S. Chauhan, Shivanand

“…The model characterizes inventories with three unique demand patterns by analytically solving ordinary differential equations through Maclaurin series approximations. …”
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Numerical analysis of mathematical model of nanofluid flow through stagnation point involving thermal radiation, activation energy, and living organisms by Munaza Chaudhry, Muhammad Abdul Basit, Muhammad Imran, Madeeha Tahir, Aiedh Mrisi Alharthi, Jihad Younis

“…Nonlinear partial differential equations are transformed into a collection of linked ordinary differential equations via similarity transformations. …”
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Design of Morlet Wavelet Neural Networks for Solving the Nonlinear Van der Pol–Mathieu–Duffing Oscillator Model by Ali Hasan Ali, Muhammad Amir, Jamshaid Ul Rahman, Ali Raza, Ghassan Ezzulddin Arif

“…We develop an MWNN-based fitness function to predict the dynamic behavior of nonlinear Vd-PM-DO differential equations. Then, we apply a novel hybrid approach combining WCA and ABC to optimize this fitness function, and determine the optimal weight and biases for MWNN. …”
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Ecology through the eyes of a non-ecologist by Janusz Uchmański

“…It allows the use of traditional difference and differential equations in the formulation of mathematical models, which has proven itself in practical applications many times.…”
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A Two-Fluid Conditional Averaging Paradigm for the Theory and Modeling of Turbulent Premixed Combustion by Vladimir L. Zimont

“…These equations are necessary for the development of model differential equations for the Reynolds stresses and the chemical source in the advanced modeling and simulation of turbulent premixed combustion. …”
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Mathematical modeling in autoimmune diseases: from theory to clinical application by Yaroslav Ugolkov, Yaroslav Ugolkov, Yaroslav Ugolkov, Antonina Nikitich, Antonina Nikitich, Cristina Leon, Gabriel Helmlinger, Kirill Peskov, Kirill Peskov, Kirill Peskov, Kirill Peskov, Victor Sokolov, Victor Sokolov, Alina Volkova, Alina Volkova

“…. ≥70% of the models were developed as nonlinear systems of ordinary differential equations, others – as partial differential equations, integro-differential equations, Boolean networks, or probabilistic models. …”
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Comment on “Variational Iteration Method for Fractional Calculus Using He’s Polynomials” by Ji-Huan He

“…A standard variational iteration algorithm for fractional differential equations is suggested.…”
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