A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach by Taha Aziz, F. M. Mahomed

“…In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. …”
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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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Registration-Based Morphing of Active Contours for Segmentation of CT Scans by Yuan-Nan Young, Doron Levy

“…We present a new algorithm for segmenting organs in CT scans forradiotherapy treatment planning.Given a contour of an organ that is segmentedin one image, our algorithm proceeds tosegment contours that identify the same organ inthe consecutive images.Our technique combines partial differential equations-based morphing activecontours with algorithms for joint segmentation and registration. …”
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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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Maximal regular boundary value problems in Banach-valued function spaces and applications by Veli B. Shakhmurov

“…In applications, the nonlocal boundary value problems for quasi elliptic partial differential equations, nonlocal initial boundary value problems for parabolic equations, and their systems on cylindrical domain are studied.…”
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Novel exact solutions for PDEs with mixed boundary conditions by Mark Craddock, Martino Grasselli, Andrea Mazzoran

“…Abstract We develop methods for the solution of inhomogeneous Robin-type boundary value problems (BVPs) that arise for certain linear parabolic partial differential equations (PDEs) on a half-line, as well as a second-order generalization. …”
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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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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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Generalized Hyperbolic Function Solution to a Class of Nonlinear Schrödinger-Type Equations by Zeid I. A. Al-Muhiameed, Emad A.-B. Abdel-Salam

“…With the help of the generalized hyperbolic function, the subsidiary ordinary differential equation method is improved and proposed to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. A class of nonlinear Schrödinger-type equations including the generalized Zakharov system, the Rangwala-Rao equation, and the Chen-Lee-Liu equation are investigated and the exact solutions are derived with the aid of the homogenous balance principle and generalized hyperbolic functions. …”
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Construction of a Class of Copula Using the Finite Difference Method by Remi Guillaume Bagré, Frédéric Béré, Vini Yves Bernadin Loyara

“…For this, we use the finite difference method which is a common technique for finding approximate solutions of partial differential equations which consists in solving a system of relations (numerical scheme) linking the values of the unknown functions at certain points sufficiently close to each other.…”
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Two-Degree Vibration Analysis of a Horizontal Axis Turbine Blade by Finite Differential Methods by Youfeng Zhu, Hongyu Zang, Xiaofei Kong, Peng Ban

“…Two-degree vibration partial differential equations of large horizontal axis turbine blades were established by Kallesøe’s model and Greenberg unsteady aerodynamic theory. …”
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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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Positive Solutions of a General Discrete Dirichlet Boundary Value Problem by Xinfu Li, Guang Zhang

“…To the best of our knowledge, they are better than the results of the corresponding partial differential equations. In particular, the methods of proof are different.…”
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Solving the Linear 1D Thermoelasticity Equations with Pure Delay by Denys Ya. Khusainov, Michael Pokojovy

“…We propose a system of partial differential equations with a single constant delay τ>0 describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval of R1. …”
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Mean-periodic functions by Carlos A. Berenstein, B. A. Taylor

“…Ehrenpreis' work on partial differential equations with constant coefficients to arbitrary convolutors. …”
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Derivation of Equations for Flexible Multibody Systems in Terms of Quasi-Coordinates from the Extended Hamilton’s Principle by L. Meirovitch

“…In this article, hybrid (ordinary and partial) differential equations for flexible multibody systems are derived in terms of quasi-coordinates directly from the extended Hamilton's principle. …”
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A synthesized view of the CSF-blood barrier and its surgical implications for aging disorders by Birra Taha, Robert McGovern, Cornelius Lam, Cornelius Lam

“…We briefly review the mathematical framework for CSF transport as described by a set of well-studied partial differential equations. Moreover, we describe the major contributors of CSF flow through both diffusive and convective forces beginning at the molecular level and extending into macroscopic clinical observations. …”
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Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups by Masatomo Iwasa

“…The present study provides an extended method that is also applicable to partial differential equations. The main characteristic of the extended method is the restriction of the manifold by some constraint equations on which we search for a Lie symmetry group. …”
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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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