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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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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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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