Nonlinear Resonance Interaction between Conjugate Circumferential Flexural Modes in Single-Walled Carbon Nanotubes by Matteo Strozzi, Francesco Pellicano

“…The Rayleigh–Ritz method is applied to approximate linear eigenfunctions of the partial differential equations that govern the shell dynamics. …”
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Global Well-Posedness and Determining Nodes of Non-Autonomous Navier–Stokes Equations with Infinite Delay on Bounded Domains by Huanzhi Ge, Feng Du

“…The asymptotic behavior of solutions to nonlinear partial differential equations is an important tool for studying their long-term behavior. …”
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Modification of the Differential Transform Method With Search Direction Along the Spatial Axis by Helena Nayar, Patrick Azere Phiri

“…It is shown that the method is applicable to a wide spectrum of 1+1 partial differential equations, integro partial differential equations, and integral equations. …”
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A New Numerical Procedure for Vibration Analysis of Beam under Impulse and Multiharmonics Piezoelectric Actuators by Yassin Belkourchia, Lahcen Azrar

“…However, the DQM presents some difficulties when applied to partial differential equations involving strong singularities. …”
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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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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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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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Approximation Solutions for Local Fractional Schrödinger Equation in the One-Dimensional Cantorian System by Yang Zhao, De-Fu Cheng, Xiao-Jun Yang

“…The obtained solutions show that the present method is an efficient and simple tool for solving the linear partial differentiable equations within the local fractional derivative.…”
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A New Type of Distributed Parameter Control Systems: Two-Point Boundary Value Problems for Infinite-Dimensional Dynamical Systems by De-Xing Kong, Fa Wu

“…This survey note describes a new type of distributed parameter control systems—the two-point boundary value problems for infinite-dimensional dynamical systems, particularly, for hyperbolic systems of partial differential equations of second order, some of the discoveries that have been done about it and some unresolved questions.…”
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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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A Numerical Assessment of Time-Dependent Magneto-Convective Thermal-Material Transfer over a Vertical Permeable Plate by Mohammed Jahir Uddin, R. Nasrin

“…The nondimensional partial differential equations of continuity, momentum, energy, and concentration are discussed using appropriate transformations. …”
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A new finite difference algorithm for boundary value problems involving transmission conditions by Semih Çavuşoğlu, Oktay Sh. Mukhtarov

“…The finite difference method (FDM) is used to find an approximate solution to ordinary and partial differential equations of various type using finite difference equations to approximate derivatives. …”
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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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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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Asymptotic Solutions of Singular Perturbed Problems with an Instable Spectrum of the Limiting Operator by Burkhan T. Kalimbetov, Marat A. Temirbekov, Zhanibek O. Khabibullayev

“…The main idea of this method is based on the analysis of dual singular points of investigated equations and passage in the space of the larger dimension, what reduces to study of systems of first-order partial differential equations with incomplete initial data.…”
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Local Fractional Laplace Variational Iteration Method for Fractal Vehicular Traffic Flow by Yang Li, Long-Fei Wang, Sheng-Da Zeng, Yang Zhao

“…We discuss the line partial differential equations arising in fractal vehicular traffic flow. …”
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New Iterative Method for Fractional Gas Dynamics and Coupled Burger’s Equations by Mohamed S. Al-luhaibi

“…Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.…”
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Substantiation of asymptotical solution of weakly nonlinear hyperbolic system by Aleksandras Krylovas

“… A hyperbolic system of first order partial differential equations with small parameter and periodical initial conditions is obtained. …”
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New Iterative Method: An Application for Solving Fractional Physical Differential Equations by A. A. Hemeda

“…The new iterative method with a powerful algorithm is developed for the solution of linear and nonlinear ordinary and partial differential equations of fractional order as well. The analysis is accompanied by numerical examples where this method, in solving them, is used without linearization or small perturbation which con…firm the power, accuracy, and simplicity of the given method compared with some of the other methods.…”
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