Null Controllability of a Four Stage and Age-Structured Population Dynamics Model by Amidou Traoré, Bedr’Eddine Ainseba, Oumar Traoré

“…Our method combines fixed point theorem and Carleman estimate. We end this work with numerical illustrations.…”
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Existence and Uniqueness of Solutions for Fractional Boundary Value Problems under Mild Lipschitz Condition by Imed Bachar, Habib Mâagli, Hassan Eltayeb

“…Based on the Banach fixed point theorem on an appropriate space, we prove that this problem possesses a unique continuous solution u satisfying ut≤cωt,for t∈0,1 and c>0, where ωt≔tα−21−t2.…”
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Existence of Solutions for Boundary Value Problem of a Caputo Fractional Difference Equation by Zhiping Liu, Shugui Kang, Huiqin Chen, Jianmin Guo, Yaqiong Cui, Caixia Guo

“…We use Schauder fixed point theorem to deduce the existence of solutions. …”
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Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations by Yige Zhao, Shurong Sun, Zhenlai Han, Qiuping Li

“…By the properties of the Green function and Guo-Krasnosel'skii fixed point theorem on cones, the eigenvalue intervals of the nonlinear fractional differential equation boundary value problem are considered, some sufficient conditions for the nonexistence and existence of at least one or two positive solutions for the boundary value problem are established. …”
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Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type by Hsiang Liu, Cheng-Wen Liao, Chin-Tzong Pang

“…We first employ the Schauder fixed-point theorem to prove the existence of solution on the interval for that is small enough, and, then, by letting and using a diagonal argument, we have the existence results on the interval . …”
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Nearly Quadratic n-Derivations on Non-Archimedean Banach Algebras by Madjid Eshaghi Gordji, Badrkhan Alizadeh, Young Whan Lee, Gwang Hui Kim

“…We investigate the Hyers-Ulam stability of quadratic n-derivations from non-Archimedean Banach algebras into non-Archimedean Banach modules by using the Banach fixed point theorem.…”
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Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument by Xuemei Zhang, Meiqiang Feng

“…Furthermore, several new and more general results are obtained for the existence of positive solutions for the above problem by using Krasnosel’skii’s fixed point theorem. We discuss our problems with a delayed argument, which may concern optimization issues of some technical problems. …”
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The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems by Yuanyuan Pan, Zhenlai Han, Shurong Sun, Yige Zhao

“…The existence of solutions to this problem is established by the Guo-Krasnosel'kii theorem and the Schauder fixed-point theorem, and some examples are given to illustrate the main results.…”
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On Multivalued Fuzzy Contractions in Extended b-Metric Spaces by Nayab Alamgir, Quanita Kiran, Hassen Aydi, Yaé Ulrich Gaba

“…Thereafter, we introduce the concept of multivalued fuzzy contraction mappings and prove related α-fuzzy fixed point theorems in the context of extended b-metric spaces that generalize Nadler’s fixed point theorem as well as many preexisting results in the literature. …”
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Multistability and Instability of Competitive Neural Networks with Mexican-Hat-Type Activation Functions by Xiaobing Nie, Jinde Cao, Shumin Fei

“…By tracking the dynamics of each state component and applying fixed point theorem and analysis method, some sufficient conditions are presented to study the multistability and instability, including the total number of equilibria, their locations, and local stability and instability. …”
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Spatial and Temporal Dynamics of a Viral Infection Model with Two Nonlocal Effects by Xiaoyan Wang, Yuming Chen, Junyuan Yang

“…Then we obtain the existence of endemic steady states by Shauder fixed point theorem. A threshold dynamics is established by the approach of Lyapunov functionals. …”
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Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary Conditions by Thanin Sitthiwirattham, Jessada Tariboon, Sotiris K. Ntouyas

“…The existence of at least one solution is proved by using Krasnoselskii's fixed point theorem and Leray-Schauder's nonlinear alternative. …”
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Iterative Analysis of the Unique Positive Solution for a Class of Singular Nonlinear Boundary Value Problems Involving Two Types of Fractional Derivatives with p-Laplacian Operator by Fang Wang, Lishan Liu, Yonghong Wu, Yumei Zou

“…Based on the method of reducing the order of fractional derivative, some properties of the corresponding Green’s function, and the fixed point theorem of mixed monotone operator, an interesting result on the iterative sequence of the uniqueness of positive solutions is obtained under the assumption that the nonlinear term may be singular in regard to both the time variable and space variables. …”
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A Fast Numerical Method for the Calculation of the Equilibrium Isotopic Composition of a Transmutation System in an Advanced Fuel Cycle by F. Álvarez-Velarde, E. M. González-Romero

“…A fast numerical method for the calculation in a zero-dimensional approach of the equilibrium isotopic composition of an iteratively used transmutation system in an advanced fuel cycle, based on the Banach fixed point theorem, is described in this paper. The method divides the fuel cycle in successive stages: fuel fabrication, storage, irradiation inside the transmutation system, cooling, reprocessing, and incorporation of the external material into the new fresh fuel. …”
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Constructive Existence of (1,1)-Solutions to Two-Point Value Problems for Fuzzy Linear Multiterm Fractional Differential Equations by HuiChol Choi, SungHyok Kwon, Kinam Sin, Sunae Pak, Sungryol So

“…Our existence result is based on Banach fixed point theorem and the approximate solution of our problem is obtained by applying the Haar wavelet operational matrix.…”
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Some Rational Coupled Fuzzy Cone Contraction Theorems in Fuzzy Cone Metric Spaces with an Application by Saif Ur Rehman, Muhammad Talha Waheed, Naeem Jan, Abdu Gumaei, Mabrook Al-Rakhami

“…Furthermore, we present an application of a Lebesgue integral-type contraction mapping in fuzzy cone metric spaces and to prove a unique coupled fixed-point theorem.…”
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Dynamic Processes, Fixed Points, Endpoints, Asymmetric Structures, and Investigations Related to Caristi, Nadler, and Banach in Uniform Spaces by Kazimierz Włodarczyk, Robert Plebaniak

“…Moreover, using these new structures, the single-valued contractions of two kinds of Banach type are defined and the new and general versions of the Banach uniqueness and iterate approximation of fixed point theorem for uniform spaces are established. …”
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New Results for Some Intuitionistic Fuzzy Partial Functional Differential Equations with State-Dependent Delay by Bouchra Ben Amma, Said Melliani, Lalla Saadia Chadli

“…The main results of this paper are based on the Banach fixed point theorem. An illustrated example of our results is given with some numerical simulations for $\beta$-cuts of the intuitionistic fuzzy solutions.…”
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On the Existence and Stability of Positive Solutions of Eigenvalue Problems for a Class of P-Laplacian ψ-Caputo Fractional Integro-Differential Equations by Yahia Awad

“…The study utilizes various techniques, including the analysis of Green’s function properties and the application of Guo–Krasnovelsky’s fixed point theorem on cones. By employing these methods, the research establishes novel findings concerning the existence and nonexistence of positive solutions. …”
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Existence and Uniqueness Results for a Class of Singular Fractional Boundary Value Problems with the p-Laplacian Operator via the Upper and Lower Solutions Approach by KumSong Jong, HuiChol Choi, KyongJun Jang, SunAe Pak

“…Here, the nonlinear source term f permits singularity with respect to its time variable t. Some fixed-point theorems such as the Leray-Schauder nonlinear alternative, the Schauder fixed-point theorem, and the Banach contraction mapping principle and the properties of the Gauss hypergeometric function are used to prove our main results. …”
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