Benjamin-Ono Equation on a Half-Line by Nakao Hayashi, Elena I. Kaikina

“…We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time.…”
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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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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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Existence Theorems for Fractional Semilinear Integrodifferential Equations with Noninstantaneous Impulses and Delay by Bo Zhu, Minhui Zhu

“…An example involving partial differential equations with noninstantaneous impulses is given to show the application of our main results.…”
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On the correct formulation of a nonlinear differential equations in Banach space by Mahmoud M. El-Borai, Osama L. Moustafa, Fayez H. Michael

“…We also give an application of the theory of partial differential equations.…”
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Function Spaces with a Random Variable Exponent by Boping Tian, Yongqiang Fu, Bochi Xu

“…After discussing the properties of the spaces 𝐿𝑝(𝜔)(𝐷×Ω) and 𝑊𝑘,𝑝(𝜔)(𝐷×Ω), we give an application of these spaces to the stochastic partial differential equations with random variable growth.…”
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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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Exact Solutions for the Conformable Space-Time Fractional Zeldovich Equation with Time-Dependent Coefficients by Sami Injrou

“…The study shows that the used method is effective and reliable and can be utilized as a substitution to construct new solutions of different types of nonlinear conformable fractional partial differential equations (NFPDEs) with variable coefficients.…”
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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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Gluing for the Einstein constraint equations by Corvino, Justin

“…Initial data for the Einstein equations must satisfy a system of nonlinear partial differential equations, the Einstein constraint 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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Nonlinear elliptic problems with the method of finite volumes by Sanjay Kumar Khattri

“…Numerically solving nonlinear partial differential equations consists of discretizing the nonlinear partial differential equation and then solving the formed nonlinear system of equations. …”
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On the Exact Solutions of Nonlinear Potential Yu–Toda–Sasa–Fukuyama Equation by Different Methods by Qinghao Zhu, Jianming Qi

“…It is observed that the extended complex method and G′/G-expansion method are reliable and will be used extensively to seek for exact solutions of any other nonlinear partial differential equations (NPDEs).…”
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A therapy inactivating the tumor angiogenic factors by Cristian Morales-Rodrigo

“…This paper is devoted to a nonlinear system of partial differential equations modeling the effect of an anti-angiogenic therapy based on an agent that binds to the tumor angiogenic factors. …”
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Almost Automorphic Mild Solutions to Neutral Parabolic Nonautonomous Evolution Equations with Nondense Domain by Zhanrong Hu, Zhen Jin

“…A unified framework is set up to investigate the existence and uniqueness of almost automorphic mild solutions to some classes of parabolic partial differential equations and neutral functional differential equations.…”
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Global Stability for Fractional Diffusion Equations in Biological Systems by Khalid Hattaf, Noura Yousfi

“…This paper proposes a new method of construction of Lyapunov functionals for the dynamical systems described by fractional differential equations and fractional partial differential equations. The proposed method is rigorously presented. …”
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Some Properties and Applications of a New General Triple Integral Transform “Gamar Transform’’ by Abdelilah Kamal H. Sedeeg

“…Moreover, the proposed new transform is applied to solve some partial differential equations (PDEs) such as Laplace, Mboctara, and Wave equations. …”
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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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Nonstationary Fronts in the Singularly Perturbed Power-Society Model by M. G. Dmitriev, A. A. Pavlov, A. P. Petrov

“…The theory of contrasting structures in singularly perturbed boundary problems for nonlinear parabolic partial differential equations is applied to the research of formation of steady state distributions of power within the nonlinear “power-society” model. …”
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W2,p-Solvability of the Dirichlet Problem for Elliptic Equations with Singular Data by Loredana Caso, Roberta D’Ambrosio, Maria Transirico

“…We give an overview on some results concerning the unique solvability of the Dirichlet problem in W2,p, p>1, for second-order linear elliptic partial differential equations in nondivergence form and with singular data in weighted Sobolev spaces. …”
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