Double Periodic Wave Solutions of the (2 + 1)-Dimensional Sawada-Kotera Equation by Zhonglong Zhao, Yufeng Zhang, Tiecheng Xia

“…Based on a general Riemann theta function and Hirota’s bilinear forms, we devise a straightforward way to explicitly construct double periodic wave solution of (2+1)-dimensional nonlinear partial differential equation. The resulting theory is applied to the (2+1)-dimensional Sawada-Kotera equation, thereby yielding its double periodic wave solutions. …”
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Exponential Stability of Periodic Solutions for Inertial Type BAM Cohen-Grossberg Neural Networks by Chunfang Miao, Yunquan Ke

“…First, by properly choosing variable substitution, the system is transformed to first order differential equation. Second, some sufficient conditions that ensure the existence and exponential stability of periodic solutions for the system are obtained by constructing suitable Lyapunov functional and using differential mean value theorem and inequality technique. …”
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Comparison of Analytical Solution of DGLAP Equations for... by Neelakshi N. K. Borah, D. K. Choudhury, P. K. Sahariah

“…The DGLAP equation for the nonsinglet structure function F 2 N S ( x , t ) at LO is solved analytically at low x by converting it into a partial differential equation in two variables: Bjorken x and t    ( t = l n ( Q 2 / Λ 2 ) and then solved by two methods: Lagrange’s auxiliary method and the method of characteristics. …”
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Global attractor for the lattice dynamical system of a nonlinear Boussinesq equation by Ahmed Y. Abdallah

“…As far as we are aware, our result here is the first concerning the lattice dynamical system corresponding to a differential equation of second order in time variable and fourth order in spatial variable with nonlinearity involving the gradients.…”
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Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation by Robert Willie

“…In the linear case, we show in a given sense that the asymptotic behaviour of solutions verifies a second-order ordinary differential equation. In the semilinear case, under suitable dissipative assumptions on the nonlinear term, we prove the existence of a global attractor for fixed diffusion and that the limiting attractor for large diffusion is finite dimensional.…”
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A Nonlinear Implicit Fractional Equation with Caputo Derivative by Ameth Ndiaye

“…In this paper, we study a nonlinear implicit differential equation with initial conditions. The considered problem involves the fractional Caputo derivatives under some conditions on the order. …”
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Higher Integrability of Weak Solutions to a Class of Double Obstacle Systems by Zhenhua Hu, Shuqing Zhou

“…We first introduce double obstacle systems associated with the second-order quasilinear elliptic differential equation div(A(x,∇u))=div f(x,u), where A(x,∇u), f(x,u) are two n×N matrices satisfying certain conditions presented in the context, then investigate the local and global higher integrability of weak solutions to the double obstacle systems, and finally generalize the results of the double obstacle problems to the double obstacle systems.…”
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Axisymmetric Longitudinal-Bending Waves in a Cylindrical Shell Interacting with a Nonlinear Elastic Medium by Alexander I. Zemlyanukhin, Andrey V. Bochkarev, Lev I. Mogilevich, Ekaterina G. Tindova

“…A nonlinear differential equation is derived which describes the propagation of axisymmetric stationary longitudinal-bending waves in infinite cylindrical shell of Timoshenko type, interacting with the external nonlinear elastic medium. …”
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Solution of the Falkner–Skan Equation Using the Chebyshev Series in Matrix Form by Abdelrady Okasha Elnady, M. Fayek Abd Rabbo, Hani M. Negm

“…A numerical method for the solution of the Falkner–Skan equation, which is a nonlinear differential equation, is presented. The method has been derived by truncating the semi-infinite domain of the problem to a finite domain and then expanding the required approximate solution as the elements of the Chebyshev series. …”
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Existence Results of Langevin Equations with Caputo–Hadamard Fractional Operator by Sombir Dhaniya, Anoop Kumar, Aziz Khan, Thabet Abdeljawad, Manar A. Alqudah

“…In this manuscript, we deal with a nonlinear Langevin fractional differential equation that involves the Caputo–Hadamard and Caputo fractional operators, with nonperiodic and nonlocal integral boundary conditions. …”
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A Novel Homotopy Perturbation Method with Applications to Nonlinear Fractional Order KdV and Burger Equation with Exponential-Decay Kernel by Shabir Ahmad, Aman Ullah, Ali Akgül, Manuel De la Sen

“…We derive an algorithm for the solution of Caputo-Fabrizio (CF) fractional order partial differential equation in series form and show its convergence to the exact solution. …”
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The Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier Method by Yousef Alnafisah

“…In this paper we describe how the Fourier series expansion of Wiener process can be used to simulate a two-dimensional stochastic differential equation (SDE) using Matlab program. Our numerical experiments use Matlab to show how our truncation of Itô’-Taylor expansion at an appropriate point produces Milstein method for the SDE.…”
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On Extended b-Rectangular and Controlled Rectangular Fuzzy Metric-Like Spaces with Application by Naeem Saleem, Salman Furqan, Fahd Jarad

“…As an application, we utilize our main results to solve the uniqueness of the solution of a differential equation occurring in the dynamic market equilibrium.…”
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Control of Hopf Bifurcation and Chaos in a Delayed Lotka-Volterra Predator-Prey System with Time-Delayed Feedbacks by Huitao Zhao, Yaowei Sun, Zhen Wang

“…A delayed Lotka-Volterra predator-prey system with time delayed feedback is studied by using the theory of functional differential equation and Hassard’s method. By choosing appropriate control parameter, we investigate the existence of Hopf bifurcation. …”
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DYNAMIC STABILITY ANALYSIS OF ADVANCED SUPPORT EQUIPMENT by XIE Miao, ZHAO ChunXiao, BAI YaJing

“…Advanced support equipment is used for comprehensive tunneling roadway temporary support equipment,in order to improve the stability and optimize the structure of the advanced support equipment,carry on the dynamic stability analysis,establish advanced support equipment mainly for components-column dynamics model,and establish the parameters of the vibration differential equation,its dynamic stability region and the dynamic instability region,using the energy method to analyze the stability of the columns,to provide the basis for advanced support equipment dynamic stability criterion later.…”
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Exact Solutions of the Time Fractional BBM-Burger Equation by Novel (G′/G)-Expansion Method by Muhammad Shakeel, Qazi Mahmood Ul-Hassan, Jamshad Ahmad, Tauseef Naqvi

“…This equation can be converted into an ordinary differential equation by using a persistent fractional complex transform and, as a result, hyperbolic function solutions, trigonometric function solutions, and rational solutions are attained. …”
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Dual Approximate Solutions of the Unsteady Viscous Flow over a Shrinking Cylinder with Optimal Homotopy Asymptotic Method by Vasile Marinca, Remus-Daniel Ene

“…The nonlinear differential equation is obtained by means of the similarity transformation. …”
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Stability of a positive equilibrium state for a stochastically perturbed mathematical model ofglassy-winged sharpshooter population by Leonid Shaikhet

“…A necessary and sufficient condition for asymptotic mean square stability of the equilibrium point of the linear part of the considered stochastic differential equation is obtained. This condition is at the same time a sufficient one for stability in probability of the equilibrium point of the initial nonlinear equation. …”
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The Role of Numerical Methods in the Sensitivity Analysis of a Density Parameter in a Passivation Rate Interaction by EN Ekaka-a, EO Chukwuocha, NM Nafo

“…The mathematical modelling of physiochemical interaction in the framework of industrial and environmental physics which relies on an initial value problem is defined by a first order ordinary differential equation. Two numerical methods of studying sensitivity analysis of physiochemical interaction data are developed. …”
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A Pest Management Model with Stage Structure and Impulsive State Feedback Control by Guoping Pang, Zhiqing Liang, Weijian Xu, Lijie Li, Gang Fu

“…We get the sufficient condition for the existence of the order-1 periodic solution by differential equation geometry theory and successor function. …”
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