Application of Image Denoising Method Based on Two-Way Coupling Diffusion Equation in Public Security Forensics by Yiqun Wang, Changpeng He, Zhenjiang Li

“…By improving the second-order partial differential equation, a new diffusion function with better diffusion effect than the original model is constructed. …”
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MHD radiative mixed convective flow of a sodium alginate-based hybrid nanofluid over a convectively heated extending sheet with Joule heating by Yasmin Humaira, Bossly Rawan, Alduais Fuad S., Al-Bossly Afrah, Saeed Anwar

“…The physical phenomena are modeled in a nonlinear partial differential equation, which is then converted into ordinary differential equations with the help of suitable similarity variables. …”
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Physics-Informed Neural Networks for Modal Wave Field Predictions in 3D Room Acoustics by Stefan Schoder

“…PINNs are appealing since they can efficiently integrate a partial differential equation and experimental data by minimizing a loss function. …”
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Fourier method in the space of φB - distributions by V. S. Mokeichev, A. M. Sidorov

“…This offers a new perspective on the theory of solvability of linear problems, which is important for solving partial differential equations, especially equations with deviating arguments. …”
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Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems by Mohamed Hannabou, Khalid Hilal, Ahmed Kajouni

“…Some concrete applications to partial differential equations are considered. Some concrete applications to partial differential equations are considered.…”
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Higher Order Compact Finite Difference Schemes for Unsteady Boundary Layer Flow Problems by P. G. Dlamini, S. S. Motsa, M. Khumalo

“…This work extends its applications to nonlinear partial differential equations modelling unsteady boundary layer flows. …”
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Third-Order Approximate Solution of Chemical Reaction-Diffusion Brusselator System Using Optimal Homotopy Asymptotic Method by Salem Alkhalaf

“…It is observed that the method is easy to implement and quite valuable for handling nonlinear system of partial differential equations and yielding excellent results at minimum computational cost. …”
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Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type by Hsiang Liu, Cheng-Wen Liao, Chin-Tzong Pang

“…The obtained results will be applied to a class of functional partial differential equations with nonlocal conditions.…”
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Solutions of type rm for a class of singular equations by Abdullah Altin

“…We obtain all solutions of radial type for a class of singular partial differential equations of even order. The essential operators here are elliptic or ultrahyperbolic.…”
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Nonlinear differential equations and algebraic systems by Lloyd K. Williams

“…The method is variation of parameters with asymptotic series and the theory of partial differential equations.…”
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Spectral framework using modified shifted Chebyshev polynomials of the third-kind for numerical solutions of one- and two-dimensional hyperbolic telegraph equations by S. M. Sayed, A. S. Mohamed, E. M. Abo-Eldahab, Y. H. Youssri

“…The current algorithm is simple to set up and is better suited to solving certain difficult partial differential equations.…”
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An Lp-Estimate for Weak Solutions of Elliptic Equations by Sara Monsurrò, Maria Transirico

“…We prove an Lp-a priori bound, p>2, for solutions of second order linear elliptic partial differential equations in divergence form with discontinuous coefficients in unbounded domains.…”
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S-asymptotic expansion of distributions by Bogoljub Stankovic

“…This paper contains first a definition of the asymptotic expansion at infinity of distributions belonging to G′Rn, named S-asymptotic expansion, as also its properties and application to partial differential equations.…”
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Diverse Precise Traveling Wave Solutions Possessing Beta Derivative of the Fractional Differential Equations Arising in Mathematical Physics by Imran Siddique, Arshad M. Mirza, Kausar Shahzadi, M. Ali Akbar, Fahd Jarad

“…The accomplished solutions show that the presented methods are not only powerful mathematical tools for generating more solutions of nonlinear time fractional partial differential equations but also can be applied to nonlinear space-time fractional partial differential equations.…”
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Surfaces of a Constant Negative Curvature by G. M. Gharib

“…I study the geometric notion of a differential system describing surfaces of a constant negative curvature and describe a family of pseudospherical surfaces for the nonlinear partial differential equations with constant Gaussian curvature .…”
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Controllability of semilinear stochastic delay evolution equations in Hilbert spaces by P. Balasubramaniam, J. P. Dauer

“…An application to stochastic partial differential equations is given.…”
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A computational scheme of exponential integrator for fuzzy electrical boundary layer flow with variable viscosity and thermal conductivity by Muhammad Shoaib Arif, Kamaleldin Abodayeh, Yasir Nawaz

“…This study aims to d an efficient computational scheme for solving partial differential equations involving fuzzy parameters in boundary layer flow. …”
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Existence and Continuous Dependence for Fractional Partial Hyperbolic Differential Equations by Qixiang Dong, Guangxian Wu, Lanping Zhu

“…This paper is concerned with a class of fractional hyperbolic partial differential equations with the Caputo derivative. Existence and continuous dependence results of solutions are obtained under the hypothesis of the Lipschitz condition without any restriction on the Lipschitz constant. …”
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Classification of Exact Solutions for Generalized Form of Equation by Hasan Bulut

“…From here, we find some interesting results for nonlinear partial differential equations with generalized evolution.…”
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Analysis of the Physical Behavior of the Periodic Mixed-Convection Flow around a Nonconducting Horizontal Circular Cylinder Embedded in a Porous Medium by Muhammad Ashraf, Zia Ullah, Saqib Zia, Sayer O. Alharbi, Dumitru Baleanu, Ilyas Khan

“…For this purpose, a model in the form of partial differential equations is formulated, and then, the governing equations of the dimensionless model are transformed into the primitive form for integration by using primitive variable formulation. …”
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