Heterogeneous Fundamentalists in a Continuous Time Model with Delays by Luca Gori, Luca Guerrini, Mauro Sodini

“…We develop a continuous time model with heterogeneous fundamentalists, imitators, and discrete time delays. We show that nonlinear dynamic phenomena, such as coexistence of attractors and local and global bifurcations, occur due to the existence of a time gap in the process of adjustment of market prices.…”
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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. …”
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Exact Null Controllability for Fractional Nonlocal Integrodifferential Equations via Implicit Evolution System by Amar Debbouche, Dumitru Baleanu

“…We introduce a new concept called implicit evolution system to establish the existence results of mild and strong solutions of a class of fractional nonlocal nonlinear integrodifferential system, then we prove the exact null controllability result of a class of fractional evolution nonlocal integrodifferential control system in Banach space. …”
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Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model by Zhijian Wei, Meitao Le

“…We consider a class of system of nonlinear difference equations arising from mathematical models describing a discrete epidemic model. …”
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Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1A by Dongjie Gao

“…We consider the nonlinear matrix equation X=Q+A∗(X^−C)−1A, where Q is positive definite, C is positive semidefinite, and X^ is the block diagonal matrix defined by X^=diag(X,X,…,X). …”
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Solution of Sequential Hadamard Fractional Differential Equations by Variation of Parameter Technique by Mohammed M. Matar

“…Firstly, we obtain the solution of the linear equations using variation of parameter technique, and next we investigate the existence theorems of the corresponding nonlinear types using some fixed-point theorems. Finally, some examples are given to explain the theorems.…”
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Modification of the Quasilinearization Method for the Inverse Problem by Lenka Celechovská-Kozáková

“…We propose a new modification of Bellman's quasilinearization method such that at any iteration step, it works with an approximate solution of the original nonlinear system and with new approximation of parameters α(k+1) which are close enough to the previous ones. …”
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New Results for Set-Valued Mappings on Ordered Metric Spaces by F. Sabetghadam, H. P. Masiha, H. Aydi

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THE CONTACT PROBLEM STUDY OF THE SELF DUMPING TRUCK DRIVING AXLE HOUSING USING RESPONSE SURFACE METHOD by SUN YongGang

“…The finite element method is applied to the numerical simulation test of a dumping truck drive axle housing contact region,in order to reflect the non-linear mechanical property the CCD method is adopted to guide the test,the RSM is fitted according to the result of the test. the variance analysis of the RSM show that the RSM can describe clearly and significantly the nonlinear problem of the self dumping truck driving axle housing,the guiding suggestions are put forward based on the analysis of the RSM.…”
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Nonlocal Boundary Value Problems for q-Difference Equations and Inclusions by Sotiris K. Ntouyas, Jessada Tariboon

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Existence of Solutions for Fractional Integro-Differential Equation with Multipoint Boundary Value Problem in Banach Spaces by Yulin Zhao, Li Huang, Xuebin Wang, Xianyang Zhu

“…By means of the fixed-point theorem in the cone of strict-set-contraction operators, we consider the existence of a nonlinear multi-point boundary value problem of fractional integro-differential equation in a Banach space. …”
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Stability of Runge-Kutta Methods for Neutral Delay Differential Equations by Liping Wen, Xiong Liu, Yuexin Yu

“…This paper is concerned with the numerical stability of a class of nonlinear neutral delay differential equations. The numerical stability results are obtained for (k,l)-algebraically stable Runge-Kutta methods when they are applied to this type of problem. …”
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Some existence and uniqueness results for first-order boundary value problems for impulsive functional differential equations with infinite delay in Fréchet spaces by John R. Graef, Abdelghani Ouahab

“…A recent nonlinear alternative for contraction maps in Fréchet spaces due to Frigon and Granas is used to investigate the existence and uniqueness of solutions to first-order boundary value problems for impulsive functional differential equations with infinite delay. …”
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Some Identities on the High-Order -Euler Numbers and Polynomials with Weight 0 by Jongsung Choi, Hyun-Mee Kim, Young-Hee Kim

“…We construct the th order nonlinear ordinary differential equation related to the generating function of -Euler numbers with weight 0. …”
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Error Analysis of an Implicit Spectral Scheme Applied to the Schrödinger-Benjamin-Ono System by Juan Carlos Muñoz Grajales

“…We develop error estimates of the semidiscrete and fully discrete formulations of a Fourier-Galerkin numerical scheme to approximate solutions of a coupled nonlinear Schrödinger-Benjamin-Ono system that describes the motion of two fluids with different densities under capillary-gravity waves in a deep water regime. …”
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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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Research progress of chaotic secure optical communication by Lilin YI, Junxiang KE

“…For the key technologies and latest research progress on chaotic secure optical communication,chaos generation methods based on different nonlinear components were introduced firstly.Then the research progress of chaotic optical communication was discussed,including how to improve the security level,and how to increase the transmission capacity and distance of chaotic optical communication.At last,the limitations and potentials of chaotic optical communication were discussed,the key technologies and research progress of chaotic secure optical communication were summarized.…”
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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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Constrained Weak Nash-Type Equilibrium Problems by W. C. Shuai, K. L. Xiang, W. Y. Zhang

“…A constrained weak Nash-type equilibrium problem with multivalued payoff functions is introduced. By virtue of a nonlinear scalarization function, some existence results are established. …”
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Fixed Points for Contractive Mappings of Integral Type Involving ω-Distance and Applications by Haiyan Gao, Na Liu, Liangshi Zhao

“…The proved results are used to investigate the solvability of certain nonlinear integral equations. Four examples are given.…”
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