Existence Theorems for Fractional Semilinear Integrodifferential Equations with Noninstantaneous Impulses and Delay by Bo Zhu, Minhui Zhu

“…An example involving partial differential equations with noninstantaneous impulses is given to show the application of our main results.…”
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C⁎-Algebra-Valued G-Metric Spaces and Related Fixed-Point Theorems by Congcong Shen, Lining Jiang, Zhenhua Ma

“…As an application, we prove the existence and uniqueness of the solution of a type of differential equations.…”
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Exact Traveling Wave Solutions to the (2 + 1)-Dimensional Jaulent-Miodek Equation by Yongyi Gu, Bingmao Deng, Jianming Lin

“…It has presented that the applied method is very efficient and is practically well suited for the nonlinear differential equations that arise in mathematical physics.…”
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Multiple Time-Scales Analysis to Predict the Quasiperiodic Oscillatory Response of a Thin-Walled Beam Subjected to 1:1:1 Simultaneous Resonance by Ali Kandil, Y. S. Hamed, Jan Awrejcewicz, Nasser A. Saeed

“…These deflections are governed by a system of two ordinary differential equations in order to describe their Cartesian directions. …”
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A Numerical Assessment of Time-Dependent Magneto-Convective Thermal-Material Transfer over a Vertical Permeable Plate by Mohammed Jahir Uddin, R. Nasrin

“…The nondimensional partial differential equations of continuity, momentum, energy, and concentration are discussed using appropriate transformations. …”
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Computational Study on Three-Dimensional Convective Casson Nanofluid Flow past a Stretching Sheet with Arrhenius Activation Energy and Exponential Heat Source Effects by P. Ragupathi, S. Saranya, H.V.R. Mittal, Qasem M. Al-Mdallal

“…The developed model of nonlinear partial differential equations (PDEs) has been transformed into ordinary differential equations (ODEs) using similarity transformations. …”
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Dynamic Characteristics of Blade with Viscoelastic Damping Block Based on Complex Eigenvalue Method by Jiao Wang, Yue-hao Zhang, Tao Yu, Qing-kai Han

“…Then the differential equations of motion with 3-DOF are numerically solved by using complex eigenvalue method. …”
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Chemical Reaction Effects on the Flow of Titanium Dioxide–Water in a Mixed Convective Nanofluid along an Inclined Plate in a Porous Medium by Md. Nasir Uddin, Kakali Chowdhury, Jannatul Ferdows Mim

“…With the aid of a system of governing partial differential equations, a set of nonlinear ordinary differential equations for taking into consideration nanofluid flow have been derived using appropriate matching transformations. …”
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Vortex-Induced Vibration of a Cable-Stayed Bridge by M. T. Song, D. Q. Cao, W. D. Zhu

“…Orthogonality conditions of exact mode shapes of the linearized undamped cable-stayed bridge model are employed to convert coupled governing partial differential equations of the original cable-stayed bridge model with damping to a set of ordinary differential equations by using Galerkin method. …”
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New Approaches to Fractal–Fractional Bullen’s Inequalities Through Generalized Convexity by Wedad Saleh, Hamid Boulares, Abdelkader Moumen, Hussien Albala, Badreddine Meftah

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Application of artificial intelligence brain structure-based paradigm to predict the slip condition impact on magnetized thermal Casson viscoplastic fluid model under combined temp... by Umar Farooq, Shan Ali Khan, Haihu Liu, Muhammad Imran, Lotfi Ben Said, Aleena Ramzan, Taseer Muhammad

“…With the help of a similarity transformation, the complex partial differential equations governing the flow and energy take on the form of nonlinear ordinary differential equations. …”
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Nonuniform Continuity of the Osmosis K(2, 2) Equation by Aiyong Chen, Yong Ding, Wentao Huang

“…The qualitative theory of differential equations is applied to the osmosis K(2, 2) equation. …”
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Culling structured hosts to eradicate vector-borne diseases by Xinli Hu, Yansheng Liu, Jianhong Wu

“…A compartmental model is developed, in the form of a nonautonomoussystem of delay differential equations subject to impulses atspecific times, for mosquito-born disease control involvinglarvicides and insecticide sprays. …”
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Existence and Uniqueness Theorems of Ordered Contractive Map in Banach Lattices by Xingchang Li, Zhihao Wang

“…Moreover, we prove the existence of a unique solution for first-order ordinary differential equations with initial value conditions by using the theoretical results with no need for using the condition of a lower solution or an upper solution.…”
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Complete Controllability of Impulsive Fractional Linear Time-Invariant Systems with Delay by Xian-Feng Zhou, Song Liu, Wei Jiang

“…Some flaws on impulsive fractional differential equations (systems) have been found. This paper is concerned with the complete controllability of impulsive fractional linear time-invariant dynamical systems with delay. …”
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Function Spaces with a Random Variable Exponent by Boping Tian, Yongqiang Fu, Bochi Xu

“…After discussing the properties of the spaces 𝐿𝑝(𝜔)(𝐷×Ω) and 𝑊𝑘,𝑝(𝜔)(𝐷×Ω), we give an application of these spaces to the stochastic partial differential equations with random variable growth.…”
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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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Mixed convection hybrid nanofluid flow past a non-isothermal cone and wedge with radiation and convective boundary condition: Heat transfer optimization by Rusya Iryanti Yahaya, Norihan Md Arifin, Mohd Shafie Mustafa, Ioan Pop, Fadzilah Md Ali, Siti Suzilliana Putri Mohamed Isa

“…Non-linear ordinary differential equations, derived through similarity transformation of the governing partial differential equations and boundary conditions, are solved numerically using the bvp4c solver. …”
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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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Nonlinear Dynamic Behavior of Winding Hoisting Rope under Head Sheave Axial Wobbles by Guoying Wang, Xingming Xiao, Chi Ma, Gang Cheng, Xiao Di

“…The governing equations are nonlinear infinite-dimensional partial differential equations, which are discretized into the finite-dimensional ordinary differential equations through the Galerkin method. …”
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