Existence of nonoscillatory solutions for higher order nonlinear mixed neutral differential equations by Hui Li, Nana Jin, Yu Zhang

“…By means of the Schauder-Tychonoff fixed point theorem and inequality techniques, some new sufficient conditions for the existence of nonoscillatory solutions were established. …”
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Existence of Three Positive Solutions for a Class of Boundary Value Problems of Caputo Fractional q-Difference Equation by Huiqin Chen, Shugui Kang, Lili Kong, Ying Gao

“…By applying these properties and the Leggett-Williams fixed-point theorem, existence criteria of three positive solutions are obtained. …”
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Existence of Positive Solutions for Two-Point Boundary Value Problems of Nonlinear Finite Discrete Fractional Differential Equations and Its Application by Caixia Guo, Jianmin Guo, Ying Gao, Shugui Kang

“…On the other hand, by using the main properties of Green function and the Krasnoselskii fixed point theorem on cones, some sufficient conditions for the existence of at least one or two positive solutions for the boundary value problem are established.…”
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Quantitative analysis and stability results in $ \beta $-normed space for sequential differential equations with variable coefficients involving two fractional derivatives by Debao Yan

“…Banach's fixed-point principle and Shaefer's fixed-point theorem were exploited to ensure that two existence conditions of the solutions for the problems were established. …”
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Sequential Derivatives of Nonlinear q-Difference Equations with Three-Point q-Integral Boundary Conditions by Nittaya Pongarm, Suphawat Asawasamrit, Jessada Tariboon

“…By using Banach's contraction mapping, Krasnoselskii's fixed-point theorem, and Leray-Schauder degree theory, some new existence results are obtained. …”
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Solvability of a Second Order Nonlinear Neutral Delay Difference Equation by Zeqing Liu, Liangshi Zhao, Jeong Sheok Ume, Shin Min Kang

“…By means of the Krasnoselskii and Schauder fixed point theorem and some new techniques, we get the existence results of uncountably many bounded nonoscillatory, positive, and negative solutions for the equation, respectively. …”
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A Time Discontinuous Galerkin Finite Element Method for Quasi-Linear Sobolev Equations by Hong Yu, Tongjun Sun

“…The existence and uniqueness of the approximate solution are proved by use of Brouwer’s fixed point theorem. An optimal L∞(0,T;H1(Ω))-norm error estimate is derived. …”
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Functional-Type Caristi–Kirk Theorem on Menger Space and Application by Soumia Chaira, Mohammed Dahmouni, Abderrahim Eladraoui, Mustapha Kabil

“…In this paper, we extend Caristi’s fixed point theorem in metric spaces to probabilistic metric spaces, and also, we prove some common fixed point theorems for a pair of mappings satisfying a system of Caristi-type contractions in the setting of a Menger space. …”
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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. By using fixed point theorem, we obtain some new results for the existence and multiplicity of solutions to a higher-order fractional boundary value problem. …”
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Existence and Stability of Solutions for Hadamard-Stieltjes Fractional Integral Equations by Saïd Abbas, Eman Alaidarous, Mouffak Benchohra, Juan J. Nieto

“…We present two results: the first one is an existence result based on Schauder’s fixed point theorem and the second one is about the generalized Ulam-Hyers-Rassias stability.…”
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Existence and Uniqueness of Positive Solutions for a Fractional Switched System by Zhi-Wei Lv, Bao-Feng Chen

“…Our results are based on a fixed point theorem of a sum operator and contraction mapping principle. …”
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Boundary Value Problem of Nonlinear Hybrid Differential Equations with Linear and Nonlinear Perturbations by Said Melliani, Abdelati El Allaoui, Lalla Saadia Chadli

“…The existence result is constructed using the Leray–Schauder alternative, and the uniqueness is guaranteed by Banach’s fixed-point theorem. Towards the end of this paper, an example is provided to illustrate the obtained results.…”
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Solvability of Nonlinear Integral Equations of Volterra Type by Zeqing Liu, Sunhong Lee, Shin Min Kang

“…The main tools used in the proofs are some techniques in analysis and the Darbo fixed point theorem via measures of noncompactness. The results obtained in this paper extend and improve essentially some known results in the recent literature. …”
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Existence of a Unique Solution and the Hyers–Ulam-H-Fox Stability of the Conformable Fractional Differential Equation by Matrix-Valued Fuzzy Controllers by Zahra Eidinejad, Reza Saadati, Tofigh Allahviranloo, Farzad Kiani, Samad Noeiaghdam, Unai Fernandez-Gamiz

“…In this paper, we consider a conformable fractional differential equation with a constant coefficient and obtain an approximation for this equation using the Radu–Mihet method, which is derived from the alternative fixed- point theorem. Considering the matrix-valued fuzzy k-normed spaces and matrix-valued fuzzy H-Fox function as a control function, we investigate the existence of a unique solution and Hyers–Ulam-H-Fox stability for this equation. …”
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Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory by Ruofeng Rao, Shouming Zhong

“…This is the first time to employ the fixed point theorem to derive the stability criterion of reaction-diffusion impulsive stochastic CNN with distributed time delays. …”
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Existence of Solutions for Fractional q-Integrodifference Equations with Nonlocal Fractional q-Integral Conditions by Suphawat Asawasamrit, Jessada Tariboon, Sotiris K. Ntouyas

“…By applying the Banach contraction principle, Krasnoselskii’s fixed point theorem, and Leray-Schauder nonlinear alternative, the existence and uniqueness of solutions are obtained. …”
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Positive Solutions of Nonlinear Fractional Differential Equations with Integral Boundary Value Conditions by J. Caballero, I. Cabrera, K. Sadarangani

“…Our analysis relies on a fixed point theorem in partially ordered sets. Moreover, we compare our results with others that appear in the literature.…”
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Extremal Solutions for Caputo Conformable Differential Equations with p-Laplacian Operator and Integral Boundary Condition by Zhongqi Peng, Yuan Li, Qi Zhang, Yimin Xue

“…In this paper, using Banach fixed point theorem, we obtain the uniqueness of the solution of nonlinear and linear Cauchy problem with the conformable derivatives in the Caputo setting, respectively. …”
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Existence of Positive Solutions to Singular 𝑝-Laplacian General Dirichlet Boundary Value Problems with Sign Changing Nonlinearity by Qiying Wei, You-Hui Su, Subei Li, Xing-Xue Yan

“…By using the well-known Schauder fixed point theorem and upper and lower solution method, we present some existence criteria for positive solution of an 𝑚-point singular 𝑝-Laplacian dynamic equation on time scales with the sign changing nonlinearity. …”
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Approximate Controllability for Impulsive Riemann-Liouville Fractional Differential Inclusions by Zhenhai Liu, Maojun Bin

“…Secondly, by using the fractional power of operators and a fixed point theorem for multivalued maps, we establish sufficient conditions for the approximate controllability for a class of Riemann-Liouville fractional impulsive differential inclusions, which is a generalization and continuation of the recent results on this issue. …”
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