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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A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach by Taha Aziz, F. M. Mahomed

“…In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. …”
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Exact Solutions of the 3D Fractional Helmholtz Equation by Fractional Differential Transform Method by Saleh Alshammari, Salah Abuasad

“…Two examples are given to prove the proficiency of the suggested method, to resolve diverse categories of fractional partial differential equations.…”
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Registration-Based Morphing of Active Contours for Segmentation of CT Scans by Yuan-Nan Young, Doron Levy

“…We present a new algorithm for segmenting organs in CT scans forradiotherapy treatment planning.Given a contour of an organ that is segmentedin one image, our algorithm proceeds tosegment contours that identify the same organ inthe consecutive images.Our technique combines partial differential equations-based morphing activecontours with algorithms for joint segmentation and registration. …”
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Fractional-View Analysis of Space-Time Fractional Fokker-Planck Equations within Caputo Operator by Saleh Alshammari, Naveed Iqbal, Mohammad Yar

“…Compared to other methods of finding approximate and exact solutions for nonlinear partial differential equations, this technique is more efficient and time-consuming.…”
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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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Novel exact solutions for PDEs with mixed boundary conditions by Mark Craddock, Martino Grasselli, Andrea Mazzoran

“…Abstract We develop methods for the solution of inhomogeneous Robin-type boundary value problems (BVPs) that arise for certain linear parabolic partial differential equations (PDEs) on a half-line, as well as a second-order generalization. …”
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Modified Homotopy Perturbation Method for Solving Fractional Differential Equations by A. A. Hemeda

“…The modified homotopy perturbation method is extended to derive the exact solutions for linear (nonlinear) ordinary (partial) differential equations of fractional order in fluid mechanics. …”
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Applications of Karry-Kalim-Adnan Transformation (KKAT) to Mechanics and Electrical Circuits by Karry Iqbal, Muhammad Kalim, Adnan Khan

“…In this paper, we have used the new integral transformation known as Karry-Kalim-Adnan transformation (KKAT) to solve the ordinary linear differential equations as well as partial differential equations. We have used KKAT to solve the problems of engineering and sciences specially electrical and mechanical problems. …”
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