The Improved Generalized tanh-coth Method Applied to Sixth-Order Solitary Wave Equation by M. Torvattanabun, J. Simmapim, D. Saennuad, T. Somaumchan

“…This method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. The new exact solutions consisted of trigonometric functions solutions, hyperbolic functions solutions, exponential functions solutions, and rational functions solutions. …”
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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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On the Carleman classes of vectors of a scalar type spectral operator by Marat V. Markin

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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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Abundant Interaction Solutions of Sine-Gordon Equation by DaZhao Lü, YanYing Cui, ChangHe Liu, ShangWen Wu

“…The method is based upon the forms and structures of Wronskian solutions of sine-Gordon equation, and the functions used in the Wronskian determinants do not satisfy linear partial differential equations. Such interaction solutions are difficultly obtained via other methods. …”
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On the stability of the linear delay differential and difference equations by A. Ashyralyev, P. E. Sobolevskii

“…We consider the initial-value problem for linear delay partial differential equations of the parabolic type. We give a sufficient condition for the stability of the solution of this initial-value problem. …”
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Analytic solutions of a generalized complex multi-dimensional system with fractional order by Baleanu Dumitru, Ibrahim Rabha W.

“…The Duhamel principle is a mathematical principle that allows us to solve linear partial differential equations. This system is generalized by the concept of the kk-symbol fractional calculus. …”
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Numerical Solution of Poisson's Equation Using a Combination of Logarithmic and Multiquadric Radial Basis Function Networks by Mohammad Mehdi Mazarei, Azim Aminataei

“…This paper presents numerical solution of elliptic partial differential equations (Poisson's equation) using a combination of logarithmic and multiquadric radial basis function networks. …”
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Modeling of the migration of endothelial cells on bioactive micropatterned polymers by Thierry Colin, Marie-Christine Durrieu, Julie Joie, Yifeng Lei, Youcef Mammeri, Clair Poignard, Olivier Saut

“…It isbased on a system of partial differential equations ofPatlak-Keller-Segel type that describes theevolution of the cell densities. …”
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On Eigenvalues of the Generator of a C0-Semigroup Appearing in Queueing Theory by Geni Gupur

“…We describe the point spectrum of the generator of a C0-semigroup associated with the M/M/1 queueing model that is governed by an infinite system of partial differential equations with integral boundary conditions. …”
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Fixed Point Theorems of Superlinear Operators with Applications by Shaoyuan Xu, Yan Han

“…The results are applied to nonlinear integral equations and partial differential equations.…”
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The First Integral Method to the Nonlinear Schrodinger Equations in Higher Dimensions by Shoukry Ibrahim Atia El-Ganaini

“…The first integral method introduced by Feng is adopted for solving some important nonlinear partial differential equations, including the (2 + 1)-dimensional hyperbolic nonlinear Schrodinger (HNLS) equation, the generalized nonlinear Schrodinger (GNLS) equation with a source, and the higher-order nonlinear Schrodinger equation in nonlinear optical fibers. …”
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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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Vibration Suppression Control of a Flexible Gantry Crane System with Varying Rope Length by Tung Lam Nguyen, Trong Hieu Do, Hong Quang Nguyen

“…The equations of motion consist of a system of ordinary and partial differential equations. Lyapunov’s direct method is used to derive the control located at the trolley end that can precisely position the gantry payload and minimize vibrations. …”
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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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Global Existence for the 3D Tropical Climate Model with Small Initial Data in H˙1/2ℝ3∗ by Hui Zhang, Juan Xu

“…The well-posedness problem is an important but challenging research topic in nonlinear partial differential equations. In this paper, we establish a global-in-time existence result of strong solutions for small initial data in terms of the H˙1/2ℝ3 norm on three-dimensional tropical climate model with viscosities by derive a blow-up criterion combine with energy estimates. …”
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Operator Inequalities of Morrey Spaces Associated with Karamata Regular Variation by Jiajia Wang, Zunwei Fu, Shaoguang Shi, Ling Mi

“…Karamata regular variation is a basic tool in stochastic process and the boundary blow-up problems for partial differential equations (PDEs). Morrey space is closely related to study of the regularity of solutions to elliptic PDEs. …”
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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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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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A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations by Özkan Güner, Adem C. Cevikel

“…The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. …”
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