The Method of Lines for Ternary Diffusion Problems by Henryk Leszczyński, Milena Matusik

“…These equations are transformed by a discretization in space variables into systems of ordinary differential equations. The proposed ODEs satisfy the mass conservation law. …”
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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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Positive Solutions of a Generalized Nonautonomous Fractional Differential System by Mohammed S. Abdo, Heba Y. Zahran, El Sayed Yousef, Emad E. Mahmoud, Abdel-Haleem Abdel-Aty

“…In this work, we investigate the existence and uniqueness of positive solutions to a system of nonautonomous fractional differential equations. The fractional derivative of the system at hand is ψ- Riemann–Liouville fractional derivative. …”
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Application of the Multistep Generalized Differential Transform Method to Solve a Time-Fractional Enzyme Kinetics by Ahmed Alawneh

“…This enzyme-substrate reaction is formed by a system of nonlinear ordinary differential equations of fractional order. The fractional derivatives are described in the Caputo sense. …”
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Calculation of bending deflection and stresses of a pipe with flowing fluid in the case of variable ground load by Rimantas Didžgalvis, Antanas Sudintas, Irena Tiknevičienė

“…Using the methods of approximate solutions of differential equations, the analytical pipe bend dynamic expressions were given at the case, when the ground load minimises expo­nentially. …”
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Permanence for a Delayed Nonautonomous SIR Epidemic Model with Density-Dependent Birth Rate by Li Yingke, Chen Liang, Wang Kai

“…Applying some classical analysis techniques for ordinary differential equations and the method proposed by Wang (2002), the threshold value for the permanence and extinction of the model was obtained.…”
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Bifurcation of Travelling Wave Solutions of the Generalized Zakharov Equation by Masoud Mosaddeghi

“…By using bifurcation theory of planar ordinary differential equations all different bounded travelling wave solutions of the generalized Zakharov equation are classified in to different parametric regions. …”
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Calculation of pipe bend and tension in case of fluid velocity pulsation by Rimantas Didžgalvis, Antanas Sudintas, Irena Tiknevičienė

“… The mathematical model of a bend pipe with a flowing fluid at a fluid pulsation was created. By solving differential equations, an analytical expression of solution is received, which may be well used for calculation of normal tension of the pipe at different ground load quantities and flow velocity pulsation. …”
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Centralized and Decentralized Data-Sampling Principles for Outer-Synchronization of Fractional-Order Neural Networks by Jin-E Zhang

“…Using centralized and decentralized data-sampling principles and the theory of fractional differential equations, sufficient criteria about outer-synchronization of the controlled fractional-order neural networks are derived for structure-dependent centralized data-sampling, state-dependent centralized data-sampling, and state-dependent decentralized data-sampling, respectively. …”
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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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Numerical Method for a Markov-Modulated Risk Model with Two-Sided Jumps by Hua Dong, Xianghua Zhao

“…We first derive a system of differential equations for the Gerber-Shiu function. Furthermore, a numerical result is given based on Chebyshev polynomial approximation. …”
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Differential Subordinations of Arithmetic and Geometric Means of Some Functionals Related to a Sector by A. Lecko, M. Lecko

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Pseudo-Stieltjes calculus: $ \alpha- $pseudo-differentiability, the pseudo-Stieltjes integrability and applications by Caiqin Wang, Hongbin Xie, Zengtai Gong

“…The obtained results provide a framework for analyzing nonlinear differential equations.…”
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Modified Wiener equations by Will Watkins

“…This paper is concerned with a class of functional differential equations whose argument transforms are involutions. …”
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Monotonicity, Concavity, and Convexity of Fractional Derivative of Functions by Xian-Feng Zhou, Song Liu, Zhixin Zhang, Wei Jiang

“…The monotonicity of the solutions of a class of nonlinear fractional differential equations is studied first, and the existing results were extended. …”
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Symmetry and Solution of Neutron Transport Equations in Nonhomogeneous Media by Ivan Tsyfra, Tomasz Czyżycki

“…The method is also applicable to nonstationary and nonintegrable in quadratures differential equations.…”
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Algebro-Geometric Solutions of a (2+1)-Dimensional Integrable Equation Associated with the Ablowitz-Kaup-Newell-Segur Soliton Hierarchy by Xiaohong Chen

“…The (2+1)-dimensional Lax integrable equation is decomposed into solvable ordinary differential equations with the help of known (1+1)-dimensional soliton equations associated with the Ablowitz-Kaup-Newell-Segur soliton hierarchy. …”
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Positive Solutions for Singular p-Laplacian Fractional Differential System with Integral Boundary Conditions by Liping Wang, Zongfu Zhou, Hui Zhou

“…This paper investigates the existence of positive solutions for a class of singular p-Laplacian fractional differential equations with integral boundary conditions. …”
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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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Existence of Solutions for G-SFDEs with Cauchy-Maruyama Approximation Scheme by Faiz Faizullah

“…We present the Cauchy-Maruyama (CM) approximation scheme and establish the existence theory of stochastic functional differential equations driven by G-Brownian motion (G-SFDEs). …”
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