Convergence of the New Iterative Method by Sachin Bhalekar, Varsha Daftardar-Gejji

“…A new iterative method introduced by Daftardar-Gejji and Jafari (2006) (DJ Method) is an efficient technique to solve nonlinear functional equations. In the present paper, sufficiency conditions for convergence of DJM have been presented. …”
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On p-Hybrid Wardowski Contractions by Erdal Karapınar, Hassen Aydi, Andreea Fulga

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Nontrivial Solution of Fractional Differential System Involving Riemann-Stieltjes Integral Condition by Ge-Feng Yang

“…We study the existence and uniqueness of nontrivial solutions for a class of fractional differential system involving the Riemann-Stieltjes integral condition, by using the Leray-Schauder nonlinear alternative and the Banach contraction mapping principle, some sufficient conditions of the existence and uniqueness of a nontrivial solution of a system are obtained.…”
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Effective High-Order Iterative Methods via the Asymptotic Form of the Taylor-Lagrange Remainder by Isaac Fried

“…The asymptotic form of the Taylor-Lagrange remainder is used to derive some new, efficient, high-order methods to iteratively locate the root, simple or multiple, of a nonlinear function. Also derived are superquadratic methods that converge contrarily and superlinear and supercubic methods that converge alternatingly, enabling us not only to approach, but also to bracket the root.…”
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On Maximum Energy of Mechanical Systems Under Shock Disturbances by Dimitry V. Balandin

“…The method is demonstrated by calculating the maximal displacement in a second-order nonlinear system.…”
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New Iterative Method: An Application for Solving Fractional Physical Differential Equations by A. A. Hemeda

“…The new iterative method with a powerful algorithm is developed for the solution of linear and nonlinear ordinary and partial differential equations of fractional order as well. …”
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On the Coupling of the Homotopy Perturbation Method and New Integral Transform for Solving Systems of Partial Differential Equations by E. E. Eladdad, E. A. Tarif

“…This combination allows to obtain analytic and numerical solutions for linear and nonlinear systems of partial differential equations.…”
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Coupled Fixed Point Theorems with Rational Type Contractive Condition in a Partially Ordered G-Metric Space by K. Chakrabarti

“…Coupled fixed point theorems for a map satisfying mixed monotone property and a nonlinear, rational type contractive condition are established in a partially ordered G-metric space. …”
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A Study of Caputo-Hadamard-Type Fractional Differential Equations with Nonlocal Boundary Conditions by Wafa Shammakh

“…Existence and uniqueness results of positive solutions to nonlinear boundary value problems for Caputo-Hadamard fractional differential equations by using some fixed point theorems are presented. …”
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On the recursive sequence xn+1=−1/xn+A/xn−1 by Stevo Stević

“…We investigate the periodic character of solutions of the nonlinear difference equation xn+1=−1/xn+A/xn−1. We give sufficient conditions under which every positive solution of this equation converges to a period two solution. …”
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A degree theory for locally compact perturbations of Fredholm maps in Banach spaces

“…The construction is based on the Brouwer degree theory and on the notion of orientation for nonlinear Fredholm maps given by the authors in some previous papers. …”
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Dynamic Voltage Balancing Across Series-Connected 10 kV SiC JBS Diodes in Medium Voltage 3L-NPC Power Converter Having Snubberless Series-Connected 10 kV SiC MOSFETs by Sanket Parashar, Nithin Kolli, Raj Kumar Kokkonda, Ajit Kanale, Subhashish Bhattacharya, Bantval Jayant Baliga

“…This complexity is further increased by nonlinear device parameters, parasitic capacitance, and inductance in the commutation path for each of the eight 10 kV SiC <sc>mosfet</sc>s and four 10 kV SiC JBS diodes. …”
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Variable Step Size Adams Methods for BSDEs by Qiang Han

“…For backward stochastic differential equations (BSDEs), we construct variable step size Adams methods by means of Itô–Taylor expansion, and these schemes are nonlinear multistep schemes. It is deduced that the conditions of local truncation errors with respect to Y and Z reach high order. …”
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Existence of Periodic Solutions to Multidelay Functional Differential Equations of Second Order by Cemil Tunç, Ramazan Yazgan

“…Using Lyapunov-Krasovskii functional approach, we establish a new result to guarantee the existence of periodic solutions of a certain multidelay nonlinear functional differential equation of second order. …”
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On Fractional Order Hybrid Differential Equations by Mohamed A. E. Herzallah, Dumitru Baleanu

“…We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order 0<α<1. …”
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An approximation to discrete optimal feedback controls by Jinghao Zhu, Zhiqiang Zou

“…We study discrete solutions of nonlinear optimal control problems. By value functions, we construct difference equations to approximate the optimal control on each interval of small time. …”
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On oscillation of a food-limited population model with time delay by Leonid Berezansky, Elena Braverman

“…For a scalar nonlinear delay differential equation Ṅ(t) = r(t)N(t)(K − N(h(t)))/(K + s(t)N(g(t))),r(t) ≥ 0, h(t) ≤ t, g(t) ≤ t and some generalizations of this equation, we establish explicit oscillation and nonoscillation conditions. …”
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Two-Dimensional Fredholm Integro-Differential Equation with Singular Kernel and Its Numerical Solutions by Abeer M. Al-Bugami

“…In this paper, we introduce the nonlinear Fredholm integro-differential equation of the second kind with singular kernel in two-dimensional NT-DFIDE. …”
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Existence and Uniqueness of Solutions for a Fractional Order Antiperiodic Boundary Value Problem with a p-Laplacian Operator by Ruihui Huang

“…Based on the Leray-Schauder nonlinear alternative, several sufficient conditions of the existence and uniqueness of solution of the above problem are established. …”
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Approximation structures and applications to evolution equations by Adrian Duma, Cristian Vladimirescu

“…We discuss various properties of the nonlinear A-proper operators as well as a generalized Leray-Schauder principle. …”
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