A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential Equations by Shehu Maitama

“…Exact solution of linear and nonlinear fractional partial differential equations is successfully obtained using the analytical method.…”
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On the Bivariate Spectral Homotopy Analysis Method Approach for Solving Nonlinear Evolution Partial Differential Equations by S. S. Motsa

“…This paper presents a new application of the homotopy analysis method (HAM) for solving evolution equations described in terms of nonlinear partial differential equations (PDEs). The new approach, termed bivariate spectral homotopy analysis method (BISHAM), is based on the use of bivariate Lagrange interpolation in the so-called rule of solution expression of the HAM algorithm. …”
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Barcode Location in Financial Statement System Based on the Partial Differential Equation Image Recognition Algorithm by Jinghua Ning, Song Yu

“…This paper studies the problem of the barcode image location and recognition in the financial statement system and tries to apply the partial differential equation image recognition algorithm to the barcode location in the financial statement system. …”
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Numerical Algorithm for the Third-Order Partial Differential Equation with Three-Point Boundary Value Problem by Jing Niu, Ping Li

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Meshless Technique for the Solution of Time-Fractional Partial Differential Equations Having Real-World Applications by Mehnaz Shakeel, Iltaf Hussain, Hijaz Ahmad, Imtiaz Ahmad, Phatiphat Thounthong, Ying-Fang Zhang

“…In this article, radial basis function collocation scheme is adopted for the numerical solution of fractional partial differential equations. This method is highly demanding because of its meshless nature and ease of implementation in high dimensions and complex geometries. …”
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Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations by B. A. Jacobs, C. Harley

“…A computationally efficient hybridization of the Laplace transform with two spatial discretization techniques is investigated for numerical solutions of time-fractional linear partial differential equations in two space variables. The Chebyshev collocation method is compared with the standard finite difference spatial discretization and the absolute error is obtained for several test problems. …”
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Analytical and Numerical Methods for Solving Partial Differential Equations and Integral Equations Arising in Physical Models by Santanu Saha Ray, Om P. Agrawal, R. K. Bera, Shantanu Das, T. Raja Sekhar

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On the Coupling of the Homotopy Perturbation Method and New Integral Transform for Solving Systems of Partial Differential Equations by E. E. Eladdad, E. A. Tarif

“…This combination allows to obtain analytic and numerical solutions for linear and nonlinear systems of partial differential equations.…”
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Semisupervised Association Learning Based on Partial Differential Equations for Sparse Representation of Image Class Attributes by Wei Song, Guang Hu, Liuqing OuYang, Zhenjie Zhu

“…In this paper, we propose a multitask multiview semisupervised learning model based on partial differential equation random field and Hilbert independent standard probability image genus attribute model, i.e., shared semantics. …”
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Existence Results for a Class of Semilinear Fractional Partial Differential Equations with Delay in Banach Spaces by Bo Zhu, Baoyan Han, Xiangyun Lin

“…In this paper, we consider a class of nonlinear time fractional partial differential equations with delay. We obtain the existence and uniqueness of the mild solutions for the problem by the theory of solution operator and the general Banach contraction mapping principle. …”
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Application of the Natural Decomposition Method to Strongly Coupled Partial Differential Equations: The Gray-Scott Model. by Nsingwire, Godwin

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Image Enhancement of Cross-Border E-Commerce Logistics Video Surveillance Based on Partial Differential Equations by Xiaosheng Yu, Peili Wu

“…This paper introduces partial differential equations into the video surveillance image enhancement system of cross-border e-commerce logistics. …”
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Image Recognition of Pledges of Capital Stock in Small- and Medium-Sized Enterprises Based on Partial Differential Equations by Dehui Zhou

“…In this paper, we propose a partial differential equation-based image recognition method for SME financing inventory pledges and conduct detailed analysis and experiments. …”
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Denoising of Tourist Street Scene Image Based on ROF Model of Second-Order Partial Differential Equation by Xiaofeng Yang

“…The evolutionary diffusion method based on partial differential equations is helpful to improve the quality of noisy tourist street scene images. …”
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Analytical Solutions for the Nonlinear Partial Differential Equations Using the Conformable Triple Laplace Transform Decomposition Method by Shailesh A. Bhanotar, Mohammed K. A. Kaabar

“…In this paper, a novel analytical method for solving nonlinear partial differential equations is studied. This method is known as triple Laplace transform decomposition method. …”
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Mixed problem with nonlocal boundary conditions for a third-order partial differential equation of mixed type by M. Denche, A. L. Marhoune

“…We study a mixed problem with integral boundary conditions for a third-order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. …”
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Automatic Recognition Method of Letter Images in English Self-Learning Based on Partial Differential Equation Method by Yu Zhao, Shuping Du, Ran Li, Hong Yue

“…To solve this problem, this paper proposes a new recognition model of partial differential equations based on mean curvature motion. …”
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Analytical and Numerical Methods for Solving Partial Differential Equations and Integral Equations Arising in Physical Models 2014 by Santanu Saha Ray, Rasajit K. Bera, Adem Kılıçman, Om P. Agrawal, Yasir Khan

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Laplace Transform Methods for a Free Boundary Problem of Time-Fractional Partial Differential Equation System by Zhiqiang Zhou, Xuemei Gao

“…This pricing problem can be formulated as a free boundary problem of time-fractional partial differential equation (FPDE) system. Firstly, applying Laplace transform to the governing FPDEs with respect to the time variable results in second-order ordinary differential equations (ODEs) with two free boundaries. …”
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Noise Data Removal and Image Restoration Based on Partial Differential Equation in Sports Image Recognition Technology by Shi Junmei

“…Facing the low quality of image information in the process of sports, this paper proposes to remove the noise data and repair the image based on the partial differential equation system in image recognition technology. …”
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