A New Integro-Differential Equation for Rossby Solitary Waves with Topography Effect in Deep Rotational Fluids by Hongwei Yang, Qingfeng Zhao, Baoshu Yin, Huanhe Dong

“…From rotational potential vorticity-conserved equation with topography effect and dissipation effect, with the help of the multiple-scale method, a new integro-differential equation is constructed to describe the Rossby solitary waves in deep rotational fluids. …”
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Three Positive Periodic Solutions to Nonlinear Neutral Functional Differential Equations with Parameters on Variable Time Scales by Yongkun Li, Chao Wang

“…Using two successive reductions: B-equivalence of the system on a variable time scale to a system on a time scale and a reduction to an impulsive differential equation and by Leggett-Williams fixed point theorem, we investigate the existence of three positive periodic solutions to the nonlinear neutral functional differential equation on variable time scales with a transition condition between two consecutive parts of the scale (d/dt)(x(t)+c(t)x(t-α))=a(t)g(x(t))x(t)-∑j=1nλjfj(t,x(t-vj(t))), (t,x)∈T0(x),Δt|(t,x)∈S2i=Πi1(t,x)-t, Δx|(t,x)∈S2i=Πi2(t,x)-x, where Πi1(t,x)=t2i+1+τ2i+1(Πi2(t,x)) and Πi2(t,x)=Bix+Ji(x)+x,  i=1,2,….  …”
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Stochastic Maximum Principle of Near-Optimal Control of Fully Coupled Forward-Backward Stochastic Differential Equation by Maoning Tang

“…This paper first makes an attempt to investigate the near-optimal control of systems governed by fully nonlinear coupled forward-backward stochastic differential equations (FBSDEs) under the assumption of a convex control domain. …”
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Existence and Uniqueness Results for a Coupled System of Nonlinear Fractional Differential Equations with Antiperiodic Boundary Conditions by Huina Zhang, Wenjie Gao

“…This paper studies the existence and uniqueness of solutions for a coupled system of nonlinear fractional differential equations of order α,β∈(4,5] with antiperiodic boundary conditions. …”
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Positive Solutions for a Weakly Singular Hadamard-Type Fractional Differential Equation with Changing-Sign Nonlinearity by Xinguang Zhang, Lixin Yu, Jiqiang Jiang, Yonghong Wu, Yujun Cui

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Q-Differential Equations of Higher Order and Structural Properties of the Approximate Roots for q-Modified Derangements’ Polynomials by Cheon Seoung Ryoo, Jung Yoog Kang

“…The objective of this study is to find q-differential equations of higher order related to q-modified derangements’ polynomials and confirm the structure of approximation roots. …”
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Solving Nonstiff Higher-Order Ordinary Differential Equations Using 2-Point Block Method Directly by Hazizah Mohd Ijam, Mohamed Suleiman, Ahmad Fadly Nurullah Rasedee, Norazak Senu, Ali Ahmadian, Soheil Salahshour

“…We describe the development of a 2-point block backward difference method (2PBBD) for solving system of nonstiff higher-order ordinary differential equations (ODEs) directly. The method computes the approximate solutions at two points simultaneously within an equidistant block. …”
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Modelling for the Reduction and Spread Transmission of the Dynamics and Control of Zika virus Disease: Using Ordinary Differential Equations by G. Adamu, A.S. Ndagara, M. Mamuda, I.U. Omatola

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Mixed problem with nonlocal boundary conditions for a third-order partial differential equation of mixed type by M. Denche, A. L. Marhoune

“…We study a mixed problem with integral boundary conditions for a third-order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. …”
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Analytical and Numerical Methods for Solving Partial Differential Equations and Integral Equations Arising in Physical Models 2014 by Santanu Saha Ray, Rasajit K. Bera, Adem Kılıçman, Om P. Agrawal, Yasir Khan

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Approximate Solutions of Delay Differential Equations with Constant and Variable Coefficients by the Enhanced Multistage Homotopy Perturbation Method by D. Olvera, A. Elías-Zúñiga, L. N. López de Lacalle, C. A. Rodríguez

“…We expand the application of the enhanced multistage homotopy perturbation method (EMHPM) to solve delay differential equations (DDEs) with constant and variable coefficients. …”
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Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations by Qingxue Huang, Fuqiang Zhao, Jiaquan Xie, Lifeng Ma, Jianmei Wang, Yugui Li

“…In this paper, a robust, effective, and accurate numerical approach is proposed to obtain the numerical solution of fractional differential equations. The principal characteristic of the approach is the new orthogonal functions based on shifted Legendre polynomials to the fractional calculus. …”
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Analytic Solutions of a Second-Order Functional Differential Equation with a State Derivative Dependent Delay by Jiraphorn Somsuwan, Keaitsuda Maneeruk Nakprasit

“…We investigate an analytic solution of the second-order differential equation with a state derivative dependent delay of the form x″(z)=x(p(z)+bx′(z)). …”
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Studies on the differential equations of enzyme kinetics. II. bimolecular reaction: the fitting of experimental data to the simplified model by Claude Marmasse, Joseph Wiener

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On Six Solutions for m-Point Differential Equations System with Two Coupled Parallel Sub-Super Solutions by Jian Liu, Hua Su, Shuli Wang

“…Under the assumption of two coupled parallel subsuper solutions, the existence of at least six solutions for a kind of second-order m-point differential equations system is obtained using the fixed point index theory. …”
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Noise Data Removal and Image Restoration Based on Partial Differential Equation in Sports Image Recognition Technology by Shi Junmei

“…Facing the low quality of image information in the process of sports, this paper proposes to remove the noise data and repair the image based on the partial differential equation system in image recognition technology. …”
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Modelling for the Reduction and Spread Transmission of the Dynamics and Control of Zika virus Disease: Using Ordinary Differential Equations by G. Adamu, A.S. Ndagara, M. Mamuda, I.U. Omatola

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Oscillation Criteria for Solutions of Neutral Differential Equations of the Second-Order Emden-Fowler Type with Forcing Term by Jihan Saad, Hussain Ali Mohamad

“…  In this paper, the oscillation property and the asymptotic behavior of solutions of neutral second-order differential Equations of the Emden-Fowler type were studied under the influence of the coefficients of forces. …”
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Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation by Jinhua Wang, Hongjun Xiang, Yuling Zhao

“…We consider boundary value problem for nonlinear fractional differential equation D0+αu(t)+f(t,u(t))=0,  0<t<1,  n-1<α≤n,  n>3,  u(0)=u'(1)=u′′(0)=⋯=u(n-1)(0)=0, where D0+α denotes the Caputo fractional derivative. …”
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An Iterative Algorithm for Solving n-Order Fractional Differential Equation with Mixed Integral and Multipoint Boundary Conditions by Jingjing Tan, Xinguang Zhang, Lishan Liu, Yonghong Wu

“…In this paper, we consider the iterative algorithm for a boundary value problem of n-order fractional differential equation with mixed integral and multipoint boundary conditions. …”
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