Mean-periodic functions by Carlos A. Berenstein, B. A. Taylor

“…Ehrenpreis' work on partial differential equations with constant coefficients to arbitrary convolutors. …”
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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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Semianalytical Solutions of Some Nonlinear-Time Fractional Models Using Variational Iteration Laplace Transform Method by Javed Iqbal, Khurram Shabbir, Liliana Guran

“…In this work, we combined two techniques, the variational iteration technique and the Laplace transform method, in order to solve some nonlinear-time fractional partial differential equations. Although the exact solutions may exist, we introduced the technique VITM that approximates the solutions that are difficult to find. …”
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A Family of Novel Exact Solutions to 2+1-Dimensional KdV Equation by Zhen Wang, Li Zou, Zhi Zong, Hongde Qin

“…We introduce two subequations with different independent variables for constructing exact solutions to nonlinear partial differential equations. In order to illustrate the efficiency and usefulness, we apply this method to 2+1-dimensional KdV equation, which was first derived by Boiti et al. (1986) using the idea of the weak Lax pair. …”
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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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Approximate Traveling Wave Solutions of Coupled Whitham-Broer-Kaup Shallow Water Equations by Homotopy Analysis Method by M. M. Rashidi, D. D. Ganji, S. Dinarvand

“…The results show that the homotopy analysis method is an attractive method in solving the systems of nonlinear partial differential equations.…”
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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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Weyl-Euler-Lagrange Equations of Motion on Flat Manifold by Zeki Kasap

“…In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. …”
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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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Bivariate Chebyshev Polynomials to Solve Time-Fractional Linear and Nonlinear KdV Equations by Azam Zahrani, Mashaallah Matinfar, Mostafa Eslami

“…This work concerns the numerical solutions of a category of nonlinear and linear time-fractional partial differential equations (TFPDEs) that are called time-fractional inhomogeneous KdV and nonlinear time-fractional KdV equations, respectively. …”
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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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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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On Solutions to a Class of Functional Differential Equations with Time-Dependent Coefficients by Muhammad Mohsin, Syed Touqeer H. Shah, Ali A. Zaidi

“…In this paper, we study initial boundary value problems that involve functional (nonlocal) partial differential equations with variable coefficients. These problems arise in cell growth models with symmetric and asymmetric modes of division. …”
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Higher-Order Compact Finite Difference for Certain PDEs in Arbitrary Dimensions by Yan Gao, Songlin Liu

“…In addition, a fine description of the sixth-order CFD schemes is also developed for equations with constant coefficients, which is used to discuss certain partial differential equations (PDEs) with arbitrary dimensions. …”
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Asian Option Pricing with Monotonous Transaction Costs under Fractional Brownian Motion by Di Pan, Shengwu Zhou, Yan Zhang, Miao Han

“…The method of partial differential equations was used to solve this model and the analytical expressions of the Asian option value were obtained. …”
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Multiple Slip Effects on MHD Unsteady Flow Heat and Mass Transfer Impinging on Permeable Stretching Sheet with Radiation by Fazle Mabood, Stanford Shateyi

“…Suitable similarity variables are used to transform governing partial differential equations into a system of coupled nonlinear ordinary differential equations. …”
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On Stability Analysis of Linear Axially Moving Damped Beam with Elastic Foundation by Ghulam Yameen Mallah, Rajab Ali Malookani, Sajad Hussain Sandilo, Sanaullah Dehraj

“…The motion of axially moving beam in the term of transverse vibrations is expressed in the fourth-order linear and homogeneous partial differential equations with variable coefficients. The governing equations of motion are solved by using the two timescales perturbation method together with the Fourier expansion method. …”
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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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Embedding Operators in Vector-Valued Weighted Besov Spaces and Applications by Veli Shakhmurov

“…The infinite systems of the degenerate partial differential equations and Cauchy problem for system of parabolic equations are further studied in applications.…”
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Conservation Laws, Symmetry Reductions, and New Exact Solutions of the (2 + 1)-Dimensional Kadomtsev-Petviashvili Equation with Time-Dependent Coefficients by Li-hua Zhang

“…Applying the characteristic equations of the obtained symmetries, the (2 + 1)-dimensional KP equation is reduced to (1 + 1)-dimensional nonlinear partial differential equations, including a special case of (2 + 1)-dimensional Boussinesq equation and different types of the KdV equation. …”
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