A New Numerical Approach for the Laminar Boundary Layer Flow and Heat Transfer along a Stretching Cylinder Embedded in a Porous Medium with Variable Thermal Conductivity by S. Shateyi, G. T. Marewo

“…A suitable similarity transformation is employed to transform the partial differential equations corresponding to the momentum and heat equations into nonlinear ordinary differential equations. …”
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Matrix Laplace Transform Method and It Applications on Spring-Mass Systems by Syamsul Arifin

“…There are several methods to solve an initial value problem of second-order homogenous linear systems of differential equations with constant coefficients. That are elimination method and matrix method. …”
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A Fractional Epidemiological Model for Bone Remodeling Process by Muath Awadalla, Yves Yannick Yameni Noupoue, Kinda Abuasbeh

“…We finally obtained that modeling bone formation process using fractional differential equations yielded comparable results with those obtained through a system of classical differential equations. …”
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Derivation of ODEs and Bifurcation Analysis of a Two-DOF Airfoil Subjected to Unsteady Incompressible Flow by H. Alighanbari, S. M. Hashemi

“…The aeroelastic integro-differential equations of motion for the airfoil are reformulated into a system of six first-order autonomous ordinary differential equations. …”
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Research of Nonlinear Dynamic Characteristic of the Roller Movable Tooth Drive by Wang Zhigang, Pu Yunguo

“…The system nonlinear dynamics differential equations and coordinate transformation of differential equations are worked,and the non-dimensional treatment is carried out. …”
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A Note on Impulsive Fractional Evolution Equations with Nondense Domain by Zufeng Zhang, Bin Liu

“…This paper is concerned with the existence of integral solutions for nondensely defined fractional functional differential equations with impulse effects. Some errors in the existing paper concerned with nondensely defined fractional differential equations are pointed out, and correct formula of integral solutions is established by using integrated semigroup and some probability densities. …”
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The Use of Sumudu Transform for Solving Certain Nonlinear Fractional Heat-Like Equations by Abdon Atangana, Adem Kılıçman

“…We make use of the properties of the Sumudu transform to solve nonlinear fractional partial differential equations describing heat-like equation with variable coefficients. …”
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Linearization from Complex Lie Point Transformations by Sajid Ali, M. Safdar, Asghar Qadir

“…Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs) which have Lie algebras of maximum dimension d, with d≤4. …”
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High-Order Compact Implicit Difference Methods For Parabolic Equations in Geodynamo Simulation by Don Liu, Weijia Kuang, Andrew Tangborn

“…A series of compact implicit schemes of fourth and sixth orders are developed for solving differential equations involved in geodynamics simulations. …”
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Almost Automorphic Mild Solutions to Neutral Parabolic Nonautonomous Evolution Equations with Nondense Domain by Zhanrong Hu, Zhen Jin

“…A unified framework is set up to investigate the existence and uniqueness of almost automorphic mild solutions to some classes of parabolic partial differential equations and neutral functional differential equations.…”
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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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Infinite Horizon Optimal Control of Stochastic Delay Evolution Equations in Hilbert Spaces by Xueping Zhu, Jianjun Zhou

“…An optimal control problem of stochastic delay partial differential equations is also given as an example to illustrate our results.…”
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Approximate Solutions of Hybrid Stochastic Pantograph Equations with Levy Jumps by Wei Mao, Xuerong Mao

“…We investigate a class of stochastic pantograph differential equations with Markovian switching and Levy jumps. …”
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Exponential Fitted Operator Method for Singularly Perturbed Convection-Diffusion Type Problems with Nonlocal Boundary Condition by Habtamu Garoma Debela

“…This paper presents the study of singularly perturbed differential equations of convection-diffusion type with nonlocal boundary condition. …”
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Investigation of Two-Dimensional Viscoelastic Fluid with Nonuniform Heat Generation over Permeable Stretching Sheet with Slip Condition by Haroon Ur Rasheed, Zeeshan Khan, Saeed Islam, Ilyas Khan, Juan L. G. Guirao, Waris Khan

“…Here, in this research article, we have investigated an incompressible viscoelastic fluid flow over a uniform stretching surface sheet along with slip boundary conditions in the presence of porous media. The partial differential equations which govern the fluid flow are changed into ordinary differential equations through suitable similarity transformation variables. …”
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Significance of Marangoni convection in ethylene glycol base hybrid nanofluid flow with viscous dissipation through a porous medium by Ali Rehman, Ilyas Khan, Sultan Alshehery, Muhammad Sabaoon Khan

“…The authors applied appropriate transformations to convert a collection of dimension form of nonlinear partial differential equations to dimensionless form of nonlinear ordinary differential equations. …”
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Nonlinear Resonance Interaction between Conjugate Circumferential Flexural Modes in Single-Walled Carbon Nanotubes by Matteo Strozzi, Francesco Pellicano

“…The Rayleigh–Ritz method is applied to approximate linear eigenfunctions of the partial differential equations that govern the shell dynamics. An energy approach, based on Lagrange equations and series expansion of the displacements, is considered to reduce the initial partial differential equations to a set of nonlinear ordinary differential equations of motion. …”
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Integral Representation of Functions of Bounded Variation by Z. Lipcsey, I. M. Esuabana, J. A. Ugboh, I. O. Isaac

“…With Bainov’s introduction of impulsive differential equations having solutions of bounded variation, this class of functions had eventually entered into the theory of differential equations. …”
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A New Numerical Procedure for Vibration Analysis of Beam under Impulse and Multiharmonics Piezoelectric Actuators by Yassin Belkourchia, Lahcen Azrar

“…Thanks to this regularization, the resulting differential equations can be directly discretized using the DQM. …”
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Algebraic Properties of First Integrals for Scalar Linear Third-Order ODEs of Maximal Symmetry by K. S. Mahomed, E. Momoniat

“…By use of the Lie symmetry group methods we analyze the relationship between the first integrals of the simplest linear third-order ordinary differential equations (ODEs) and their point symmetries. …”
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