Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem by Wen Lian, Zhanbing Bai

“…The existence and multiplicity of positive solutions for the nonlinear fractional differential equation boundary value problem (BVP) DC0+αyx+fx,yx=0,   0<x<1, y0=y′1=y″0=0 is established, where 2<α≤3,  CD0+α is the Caputo fractional derivative, and f:0,1×0,∞⟶0,∞ is a continuous function. …”
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Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time Scales by Quanwen Lin, Baoguo Jia, Qiru Wang

“…As an application, we obtain a sufficient condition of oscillation of the second-order half-linear differential equation ([x′(t)]α)′+csintxα(t)=cos⁡t, where α=p/q, p, q are odd positive integers.…”
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The Effect of Pulse Vaccination and Treatment on SIR Epidemic Model with Media Impact by Zhi-Long He, Lin-Fei Nie

“…By using the geometry theory of differential equation and method of successor function, the existence of positive order-1 periodic solution is studied. …”
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On an Initial Boundary Value Problem for a Class of Odd Higher Order Pseudohyperbolic Integrodifferential Equations by Said Mesloub

“…This paper is devoted to the study of the well-posedness of an initial boundary value problem for an odd higher order nonlinear pseudohyperbolic integrodifferential partial differential equation. We associate to the equation n nonlocal conditions and n+1 classical conditions. …”
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A Generalized Nonlinear Gronwall-Bellman Inequality with Maxima in Two Variables by Yong Yan

“…We apply our result to a boundary value problem of a partial differential equation with maxima for uniqueness.…”
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Mathematical Model and Solution for Fingering Phenomenon in Double Phase Flow through Homogeneous Porous Media by Piyush R. Mistry, Vikas H. Pradhan, Khyati R. Desai

“…An approximate analytical solution of the governing nonlinear partial differential equation is obtained using variational iteration method with the use of Mathematica software.…”
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New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds by W. M. Abd-Elhameed, E. H. Doha, Y. H. Youssri

“…The principal idea for obtaining spectral numerical solutions for such equations is employing third- and fourth-kind Chebyshev wavelets along with the spectral collocation method to transform the differential equation with its boundary conditions to a system of linear or nonlinear algebraic equations in the unknown expansion coefficients which can be efficiently solved. …”
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Stability of hybrid composite rod to high temperatures by Yu. V. Nemirovskiy, D. V. Mokhovnev

“…The stability problem is reduced to solving a linear homogeneous differential equation with linear homogeneous boundary conditions. …”
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DYNAMIC PERFORMANCE ANALYSIS OF SCISSOR SEAT SUSPENSION SYSTEM by MA MingMing, YU HuiJie, NI WeiYu, WANG HaiHua

“…Based on D' Alembert's principle, the differential equation of the motion about the system was deduced, and the transfer function of the system was obtained by the basis of estabishing virtual equilibrium state of a seat suspension system. …”
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Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices by Gashaye Dessalew, Tesfaye Kebede, Gurju Awgichew, Assaye Walelign

“…Consistently ordered 2-cyclic matrices are obtained while finite difference method is applied to solve differential equation. Suitable theorems are introduced to verify the convergence of this proposed method. …”
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Convergence Time Calculation for Supertwisting Algorithm and Application for Nonaffine Nonlinear Systems by Jianhua Zhang, Quanmin Zhu, Yang Li

“…The convergence time of the STA is provided by calculating the solution of a differential equation instead of constructing Lyapunov function. …”
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Symmetry Analysis, Invariant Solutions, and Conservation Laws of Fractional KdV-Like Equation by Maria Ihsane El Bahi, Khalid Hilal

“…With the aid of infinitesimal symmetries, the vector fields and symmetry reductions of the equation are constructed, respectively; as a result, the invariant solutions are acquired in one case; we show that the KdV-like equation can be reduced to a fractional ordinary differential equation (FODE) which is connected with the Erdélyi-Kober functional derivative; for this kind of reduced form, we use the power series method for extracting the explicit solutions in the form of power series solution. …”
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Quasigeostrophic Equations for Fractional Powers of Infinitesimal Generators by Luciano Abadias, Pedro J. Miana

“…In this paper we treat the following partial differential equation, the quasigeostrophic equation: ∂/∂t+u·∇f=-σ-Aαf,  0≤α≤1, where (A,D(A)) is the infinitesimal generator of a convolution C0-semigroup of positive kernel on Lp(Rn), with 1≤p<∞. …”
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The Generalized Hermite Spectral Method Combined with Laplace Transform for Solution of the Time Fractional Fokker–Planck Equation by Lu-feng Yang

“…By the Laplace transform, the ordinary differential equation about the orthogonal expansion coefficient is transformed into a linear algebraic equation system, with the coefficient matrix being a tridiagonal lower triangular matrix. …”
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A model of regulatory dynamics with threshold-type state-dependent delay by Qingwen Hu

“…A general model which is an extension of the classical differential equation models with constant or zero time delays is developed to study the stability of steady state, the occurrence and stability of periodic oscillations in regulatory dynamics. …”
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Application of Asymptotic Analysis of a High-Dimensional HJB Equation to Portfolio Optimization by Lei Hu

“…The Hamilton–Jacobi–Bellman equation formulated from the optimal investment problem is a high-dimensional nonlinear partial differential equation and difficult to find its analytical or numerical solutions. …”
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Selective Extraction of Entangled Textures via Adaptive PDE Transform by Yang Wang, Guo-Wei Wei, Siyang Yang

“…Selective extraction of entangled textures is a challenging task due to spatial entanglement, orientation mixing, and high-frequency overlapping. The partial differential equation (PDE) transform is an efficient method for functional mode decomposition. …”
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Disease dynamics for the hometown of migrant workers by Ram P. Sigdel, C. Connell McCluskey

“…Biol. 300:100--109 (2012) formulatedand studied a delay differential equation model for disease dynamics in a region where a portionof the population leaves to work in a different region for an extended fixed period. …”
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Dynamical Analysis for the Hybrid Network Model of Delayed Predator-Prey Gompertz Systems with Impulsive Diffusion between Two Patches by Li Xiang, Yurong Zhang, Dan Zhang, Zhichun Yang, Lingzhi Huang

“…Furthermore, by employing the theory of delay functional and impulsive differential equation, we obtain sufficient condition with time delay for the permanence of the network.…”
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Positive Solutions for the Initial Value Problems of Fractional Evolution Equation by Yue Liang, Yu Ma, Xiaoyan Gao

“…As an example, we study the partial differential equation of parabolic type of fractional order.…”
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