Derivation of Equations for Flexible Multibody Systems in Terms of Quasi-Coordinates from the Extended Hamilton’s Principle by L. Meirovitch

“…In this article, hybrid (ordinary and partial) differential equations for flexible multibody systems are derived in terms of quasi-coordinates directly from the extended Hamilton's principle. …”
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Asymptotic Solutions of Singular Perturbed Problems with an Instable Spectrum of the Limiting Operator by Burkhan T. Kalimbetov, Marat A. Temirbekov, Zhanibek O. Khabibullayev

“…The main idea of this method is based on the analysis of dual singular points of investigated equations and passage in the space of the larger dimension, what reduces to study of systems of first-order partial differential equations with incomplete initial data.…”
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Pricing multi-asset financial derivatives with time-dependent parameters—Lie algebraic approach by C. F. Lo, C. H. Hui

“…Exploiting the dynamical symmetry of the pricing partial differential equations of the financial derivatives, the new method enables us to derive analytical closed-form pricing formulae very straightforwardly. …”
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Maximal regular boundary value problems in Banach-valued function spaces and applications by Veli B. Shakhmurov

“…In applications, the nonlocal boundary value problems for quasi elliptic partial differential equations, nonlocal initial boundary value problems for parabolic equations, and their systems on cylindrical domain are studied.…”
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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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Error Analysis of Galerkin's Method for Semilinear Equations by Tadashi Kawanago

“…Some of our results may be applicable for investigating the quality of numerical verification methods for solutions of ordinary and partial differential equations.…”
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Application of Conformable Sumudu Decomposition Method for Solving Conformable Fractional Coupled Burger’s Equation by Hassan Eltayeb, Said Mesloub

“…It is an approximate analytical method, which can be used to solve linear and nonlinear partial differential equations. In this work, one-dimensional conformable functional Burger’s equation has been solved by applying conformable double Sumudu decomposition. …”
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Solution of Some Types of Differential Equations: Operational Calculus and Inverse Differential Operators by K. Zhukovsky

“…We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.…”
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Local Fractional Laplace Variational Iteration Method for Fractal Vehicular Traffic Flow by Yang Li, Long-Fei Wang, Sheng-Da Zeng, Yang Zhao

“…We discuss the line partial differential equations arising in fractal vehicular traffic flow. …”
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Interpolating Stabilized Element Free Galerkin Method for Neutral Delay Fractional Damped Diffusion-Wave Equation by Mostafa Abbaszadeh, Mehdi Dehghan, Mahmoud A. Zaky, Ahmed S. Hendy

“…A numerical solution for neutral delay fractional order partial differential equations involving the Caputo fractional derivative is constructed. …”
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A Generalized Approach of Triple Integral Transforms and Applications by Rania Saadeh

“…We apply the general triple transform to solve some applications of various types of partial differential equations. The strength of the new approach is that it covers almost all integral transforms of order one, two, and three, and hence no need to find new formulas of triple integral transforms or to study the basic properties.…”
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Positive Solutions of a General Discrete Dirichlet Boundary Value Problem by Xinfu Li, Guang Zhang

“…To the best of our knowledge, they are better than the results of the corresponding partial differential equations. In particular, the methods of proof are different.…”
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On some classes of almost periodic functions in abstract spaces by Dariusz Bugajewski, Gaston M. N'Guérékata

“…Some applications to ordinary as well as partial differential equations are presented. Moreover, we introduce the class of the so-called asymptotically C(n)-almost periodic functions and give some of their properties.…”
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The Small Time Asymptotics of SPDEs with Reflection by Juan Yang, Jianliang Zhai, Qing Zhou

“…We study stochastic partial differential equations with singular drifts and with reflection, driven by space-time white noise with nonconstant diffusion coefficients under periodic boundary conditions. …”
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A Multiresolution PDE-Based Deformable Surface for Medical Imaging Applications

“…<p>We recently developed a multiresolution PDE-based deformable surface whose deformation behavior is governed by partial differential equations (PDEs) such as the weighted minimal surface flow. …”
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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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Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups by Masatomo Iwasa

“…The present study provides an extended method that is also applicable to partial differential equations. The main characteristic of the extended method is the restriction of the manifold by some constraint equations on which we search for a Lie symmetry group. …”
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Finite eigenfuction approximations for continuous spectrum operators by Robert M. Kauffman

“…The theory is designed for application to ordinary and partial differential equations; relationships between the abstract theory and differential equations are worked out in the paper. …”
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Constructions of solitary wave solutions for huge family of NPDEs with three applications. by Hanan A Alkhidhr, Y Omar

“…This study offers closed-form solutions for the frequently utilised families of nonlinear partial differential equations (NPDEs). This form based on the He's semi-inverse technique. …”
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Solving the Linear 1D Thermoelasticity Equations with Pure Delay by Denys Ya. Khusainov, Michael Pokojovy

“…We propose a system of partial differential equations with a single constant delay τ>0 describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval of R1. …”
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