Islanding Detection for Microgrid Based on Frequency Tracking Using Extended Kalman Filter Algorithm by Bin Li, Jingpeng Wang, Hailong Bao, Huiying Zhang

“…Taylor series expansion was introduced to solve nonlinear state equations. In addition, a typical microgrid model was built using MATLAB/SIMULINK. …”
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Analyzing Similarity Solution of Modified Fisher Equation by Esen Hanaç Duruk, Mehmet Emir Koksal, Ram Jiwari

“…In this paper, we first examine the type of structure of the solutions to the modified form of a nonlinear Fisher’s reaction-diffusion equation. The existence of the traveling wave solution to the equation in the long term is observed by using dynamical system theory and exhibiting a phase space analysis of its stable points. …”
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Asymptotic and numerical solutions for diffusion models for compounded risk reserves with dividend payments by S. Shao, C. L. Chang

“…After defining the process of conditional probability in finite time, martingale theory turns the nonlinear stochastic differential equation to a special class of boundary value problems defined by a parabolic equation with a nonsmooth coefficient of the convection term. …”
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Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces by Mohammed Ali Alghamdi, Naseer Shahzad, Habtu Zegeye

“…Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.…”
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Sliding Mode-Based Control of a UAV Quadrotor for Suppressing the Cable-Suspended Payload Vibration by Tom Kusznir, Jaroslaw Smoczek

“…This paper addresses the problem of damping vibrations of a cable-suspended payload during positioning of the quadrotor. A nonlinear model is derived for the coupled quadrotor-pendulum system in the X-Z plane using Euler–Lagrange formulation. …”
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On the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable Methods by A. K. Gupta, S. Saha Ray

“…Comparison between the obtained solutions with the exact solutions exhibits that both the featured methods are effective and efficient in solving nonlinear problems. The obtained results justify the applicability of the proposed methods for fractional order Burgers-Fisher and generalized Fisher’s equations.…”
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An Analytical Study of the External Environment of the Coevolution between Manufacturing and Logistics Based on the Logistic Model by Yunfei Zhou, Li Yan

“…This paper discusses the cooperative mechanism of external random interference factors on system evolution, analyzes the nonlinear variation of external environmental factors with time, and gives the estimation method. …”
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Qualitative Analyses of Fractional Integrodifferential Equations with a Variable Order under the Mittag-Leffler Power Law by Mdi Begum Jeelani, Abeer S. Alnahdi, Mohammed A. Almalahi, Mohammed S. Abdo, Hanan A. Wahash, Nadiyah Hussain Alharthi

“…This research paper intends to study some qualitative analyses for a nonlinear fractional integrodifferential equation with a variable order in the frame of a Mittag-Leffler power law. …”
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Approximate Analytical Solution for the Forced Korteweg-de Vries Equation by Vincent Daniel David, Mojtaba Nazari, Vahid Barati, Faisal Salah, Zainal Abdul Aziz

“…HAM is an approximate analytical technique which provides a novel way to obtain series solutions of such nonlinear problems. It has the auxiliary parameter ℏ, where it is easy to adjust and control the convergence region of the series solution. …”
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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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Best Proximity Point Theorem in Quasi-Pseudometric Spaces by Robert Plebaniak

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A Mathematical Model for the Dynamics of Income Distribution in the Presence of Production by Maria Letizia Bertotti

“…The framework is expressed in the form of a system of nonlinear ordinary differential equations, as many as the income classes are, involving transition probabilities. …”
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Conservation law of harmonic mappings in supercritical dimensions by Guo, Chang-Yu, Xiang, Chang-Lin

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Constructions of solitary wave solutions for huge family of NPDEs with three applications. by Hanan A Alkhidhr, Y Omar

“…This study offers closed-form solutions for the frequently utilised families of nonlinear partial differential equations (NPDEs). This form based on the He's semi-inverse technique. …”
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New Exact Solutions of Burgers’ Equation Using Power Index Method by Khalil Ahmad, Khudija Bibi

“…The proposed method has been effectively employed to find new exact solutions for the nonlinear Burgers’ equation. Finally, the proposed resulting answers are compared with the homotopy perturbation, decomposition, and variational iteration solutions.…”
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A singularly perturbed HIV model with treatment and antigenic variation by Nara Bobko, Jorge P. Zubelli

“…Using Tikhonov's theorem we prove that the model can be approximated by a lower dimensional nonlinear model. Furthermore, we show that this reduced system is globally asymptotically stable by using Lyapunov's stability theory.…”
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Method on PAPR reduction in digital beam-forming by Lu LIU, Guoqing ZHAO

“…Digital beam-forming technology is one of the key technologies in 5G communication.However,the high peak-to-average power ratio in digital beam-forming would make the power amplifier work in the nonlinear region.Nowadays,the solutions to the high peak-to-average power ratio,such as selected mapping,embedded side information selected mapping have some faults:the complexity is high,and the utilization of the bandwidth is low.A blind selected mapping method to reduce the high peak-to-average power ratio based on MUSIC algorithm was proposed.In this method,the side information was omitted,so the utilization of the bandwidth was improved.Simultaneously,the result of the peak-to-average power ratio reduction and the complexity is much more enhanced.…”
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Computational Modelling of Thermal Stability in a Reactive Slab with Reactant Consumption by O. D. Makinde

“…This paper investigates both the transient and the steady state of a one-step nth-order oxidation exothermic reaction in a slab of combustible material with an insulated lower surface and an isothermal upper surface, taking into consideration reactant consumption. The nonlinear partial differential equation governing the transient reaction-diffusion problem is solved numerically using a semidiscretization finite difference technique. …”
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Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions by Hui Li, Libo Wang, Minghe Pei

“…We investigate the existence of solutions and positive solutions for a nonlinear fourth-order differential equation with integral boundary conditions of the form x(4)(t)=f(t,x(t),x′(t),x′′(t),x′′′(t)), t∈[0,1], x(0)=x′(1)=0, x′′(0)=∫01h(s,x(s),x′(s),x′′(s))ds, x′′′(1)=0, where f∈C([0,1]×ℝ4), h∈C([0,1]×ℝ3). …”
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New Highly Efficient Families of Higher-Order Methods for Simple Roots, Permitting f′(xn)=0 by Ramandeep Behl, V. Kanwar

“…Construction of higher-order optimal and globally convergent methods for computing simple roots of nonlinear equations is an earliest and challenging problem in numerical analysis. …”
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