Multiple Solutions of Mixed Convective MHD Casson Fluid Flow in a Channel by Jawad Raza, Azizah Mohd Rohni, Zurni Omar

“…Governing partial differential equation of the proposed problem converted into nonlinear ordinary differential equations by using similarity transformation. …”
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A Class of PDEs with Nonlinear Superposition Principles by Li Peng, Liu Keying, Pan Zuliang, Zhong Weizhou

“…In the end, some applications of the PDEs are explained, which shows that the result has very subtle relations with linearization of partial differential equation.…”
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Double Periodic Wave Solutions of the (2 + 1)-Dimensional Sawada-Kotera Equation by Zhonglong Zhao, Yufeng Zhang, Tiecheng Xia

“…Based on a general Riemann theta function and Hirota’s bilinear forms, we devise a straightforward way to explicitly construct double periodic wave solution of (2+1)-dimensional nonlinear partial differential equation. The resulting theory is applied to the (2+1)-dimensional Sawada-Kotera equation, thereby yielding its double periodic wave solutions. …”
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Comparison of Analytical Solution of DGLAP Equations for... by Neelakshi N. K. Borah, D. K. Choudhury, P. K. Sahariah

“…The DGLAP equation for the nonsinglet structure function F 2 N S ( x , t ) at LO is solved analytically at low x by converting it into a partial differential equation in two variables: Bjorken x and t    ( t = l n ( Q 2 / Λ 2 ) and then solved by two methods: Lagrange’s auxiliary method and the method of characteristics. …”
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Integral price formulas for lookback options by Chenglong Xu, Yue Kuen Kwok

“…The intricacies in the derivation procedures using the partial differential equation techniques stem from the degenerate nature of the pricing models, where the lookback state variables appear only in the auxiliary conditions but not in the governing differential equations. …”
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A Novel Homotopy Perturbation Method with Applications to Nonlinear Fractional Order KdV and Burger Equation with Exponential-Decay Kernel by Shabir Ahmad, Aman Ullah, Ali Akgül, Manuel De la Sen

“…We derive an algorithm for the solution of Caputo-Fabrizio (CF) fractional order partial differential equation in series form and show its convergence to the exact solution. …”
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Qualitative Analysis of Coating Flows on a Rotating Horizontal Cylinder by Marina Chugunova, Roman M. Taranets

“…We consider a nonlinear 4th-order degenerate parabolic partial differential equation that arises in modelling the dynamics of an incompressible thin liquid film on the outer surface of a rotating horizontal cylinder in the presence of gravity. …”
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Exact Solutions of the Space Time Fractional Symmetric Regularized Long Wave Equation Using Different Methods by Özkan Güner, Dursun Eser

“…We apply the functional variable method, exp-function method, and (G′/G)-expansion method to establish the exact solutions of the nonlinear fractional partial differential equation (NLFPDE) in the sense of the modified Riemann-Liouville derivative. …”
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In Situ Bioremediation of Crude Petroleum Oil Polluted Soil Using Mathematical Experimentation by Modupe Elizabeth Ojewumi, Moses Eterigho Emetere, Damilola Elizabeth Babatunde, Joshua Olusegun Okeniyi

“…The parabolic partial differential equation developed was resolved into a system of ordinary differential equations (ODEs) by orthogonal collocation method and the necessary boundary condition was used. …”
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Basic Properties of Incomplete Macdonald Function with Applications by Jian-Jun Shu, Kunal Krishnaraj Shastri

“…This paper also shows that the incomplete Macdonald function, as a simple closed-form expression, is a particular solution to a parabolic partial differential equation, which arises naturally in a wide variety of transient and diffusion-related phenomena.…”
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On an Initial Boundary Value Problem for a Class of Odd Higher Order Pseudohyperbolic Integrodifferential Equations by Said Mesloub

“…This paper is devoted to the study of the well-posedness of an initial boundary value problem for an odd higher order nonlinear pseudohyperbolic integrodifferential partial differential equation. We associate to the equation n nonlocal conditions and n+1 classical conditions. …”
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A Generalized Nonlinear Gronwall-Bellman Inequality with Maxima in Two Variables by Yong Yan

“…We apply our result to a boundary value problem of a partial differential equation with maxima for uniqueness.…”
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Mathematical Model and Solution for Fingering Phenomenon in Double Phase Flow through Homogeneous Porous Media by Piyush R. Mistry, Vikas H. Pradhan, Khyati R. Desai

“…An approximate analytical solution of the governing nonlinear partial differential equation is obtained using variational iteration method with the use of Mathematica software.…”
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Numerical Simulation of an Air Pollution Model on Industrial Areas by Considering the Influence of Multiple Point Sources by Pravitra Oyjinda, Nopparat Pochai

“…The governing partial differential equation of air pollutant concentration is approximated by using a finite difference technique. …”
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Quasigeostrophic Equations for Fractional Powers of Infinitesimal Generators by Luciano Abadias, Pedro J. Miana

“…In this paper we treat the following partial differential equation, the quasigeostrophic equation: ∂/∂t+u·∇f=-σ-Aαf,  0≤α≤1, where (A,D(A)) is the infinitesimal generator of a convolution C0-semigroup of positive kernel on Lp(Rn), with 1≤p<∞. …”
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Application of Asymptotic Analysis of a High-Dimensional HJB Equation to Portfolio Optimization by Lei Hu

“…The Hamilton–Jacobi–Bellman equation formulated from the optimal investment problem is a high-dimensional nonlinear partial differential equation and difficult to find its analytical or numerical solutions. …”
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Selective Extraction of Entangled Textures via Adaptive PDE Transform by Yang Wang, Guo-Wei Wei, Siyang Yang

“…Selective extraction of entangled textures is a challenging task due to spatial entanglement, orientation mixing, and high-frequency overlapping. The partial differential equation (PDE) transform is an efficient method for functional mode decomposition. …”
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Positive Solutions for the Initial Value Problems of Fractional Evolution Equation by Yue Liang, Yu Ma, Xiaoyan Gao

“…As an example, we study the partial differential equation of parabolic type of fractional order.…”
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An Improved Cockroach Swarm Optimization by I. C. Obagbuwa, A. O. Adewumi

“…The original CSO was modelled with three components: chase-swarming, dispersion, and ruthless; additional hunger component which is modelled using partial differential equation (PDE) method is included in this paper. …”
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New Exact Solutions of Burgers’ Equation Using Power Index Method by Khalil Ahmad, Khudija Bibi

“…In this method, we choose suitable indexes of independent variables and similarity transformation so that the partial differential equation may be converted into ODE. We have obtained analytic solution of the ODE by using symbolic package Maple. …”
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