Positive Solutions for System of Nonlinear Fractional Differential Equations in Two Dimensions with Delay by Azizollah Babakhani

“…Our analysis relies on a nonlinear alternative of Leray-Schauder type and Krasnoselskii's fixed point theorem in a cone.…”
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Existence of Positive Periodic Solutions for a Class of Higher-Dimension Functional Differential Equations with Impulses by Zhang Suping, Jiang Wei

“…By employing the Krasnoselskii fixed point theorem, we establish some criteria for the existence of positive periodic solutions of a class of n-dimension periodic functional differential equations with impulses, which improve the results of the literature.…”
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Complete Controllability for Fractional Evolution Equations by Xia Yang, Haibo Gu

“…By contraction fixed point theorem and Krasnoselskii's fixed point theorem, we obtain some sufficient conditions to ensure the complete controllability. …”
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Existence and Uniqueness Results for Fractional Differential Equations with Riemann-Liouville Fractional Integral Boundary Conditions by Mohamed I. Abbas

“…Moreover, other existence results are also obtained by using the Krasnoselskii fixed point theorem. An example is given to illustrate the main results.…”
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Eigenvalue Problem for Nonlinear Fractional Differential Equations with Integral Boundary Conditions by Guotao Wang, Sanyang Liu, Lihong Zhang

“…By employing known Guo-Krasnoselskii fixed point theorem, we investigate the eigenvalue interval for the existence and nonexistence of at least one positive solution of nonlinear fractional differential equation with integral boundary conditions.…”
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Multiplicity Results for Variable-Coefficient Singular Third-Order Differential Equation with a Parameter by Zhibo Cheng, Yun Xin

“…By applications of Green’s function and the Krasnoselskii fixed point theorem, sufficient conditions for the existence of positive periodic solutions are established.…”
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Positive Solutions for Fourth-Order Nonlinear Differential Equation with Integral Boundary Conditions by Qi Wang, Yanping Guo, Yude Ji

“…The associated Green's function for the fourth-order boundary value problems is first given, and the arguments are based on Krasnoselskii's fixed point theorem for operators on a cone.…”
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A New Result for ψ-Hilfer Fractional Pantograph-Type Langevin Equation and Inclusions by Hamid Lmou, Khalid Hilal, Ahmed Kajouni

“…The existence and uniqueness results are obtained by making use of the Krasnoselskii fixed-point theorem and Banach contraction principle, and for the inclusion version, we use the Martelli fixed-point theorem to get the existence result. …”
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Fractional Langevin Equations with Nonseparated Integral Boundary Conditions by Khalid Hilal, Lahcen Ibnelazyz, Karim Guida, Said Melliani

“…The Banach fixed point theorem and Krasnoselskii fixed point theorem are applied to establish the results. …”
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Positive Solutions of a Fractional Boundary Value Problem with Changing Sign Nonlinearity by Yongqing Wang, Lishan Liu, Yonghong Wu

“…We first derive some properties of the associated Green function and then obtain some results on the existence of positive solutions by means of the Krasnoselskii's fixed point theorem in a cone.…”
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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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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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Results on non local impulsive implicit Caputo-Hadamard fractional differential equations by K. Venkatachalam, M. Sathish Kumar, P. Jayakumar

“…The results for a new modeling integral boundary value problem using Caputo-Hadamard impulsive implicit fractional differential equations with Banach space are investigated, along with the existence and uniqueness of solutions. The Krasnoselskii fixed-point theorem, Schaefer's fixed point theorem and the Banach contraction principle serve as the basis of this unique strategy, and are used to achieve the desired results. …”
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Existence of Positive Solution for BVP of Nonlinear Fractional Differential Equation by Jun-Rui Yue, Jian-Ping Sun, Shuqin Zhang

“…By using the well-known Guo-Krasnoselskii fixed point theorem, we obtain the existence of at least one positive solution for the above problem.…”
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Existence Theory for q-Antiperiodic Boundary Value Problems of Sequential q-Fractional Integrodifferential Equations by Ravi P. Agarwal, Bashir Ahmad, Ahmed Alsaedi, Hana Al-Hutami

“…Our results rely on the standard tools of fixed-point theory such as Krasnoselskii's fixed-point theorem, Leray-Schauder nonlinear alternative, and Banach's contraction principle. …”
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Existence of Mild Solutions for Fuzzy Fractional Evolution Equations via Krasnosel’skii Fixed Point Theorem by Ismail Airou, Ali El Mfadel, Elomari Mhamed

“…The proofs are based on fuzzy strongly continuous semigroups, a new Krasnoselskii fixed point theorem appropriate for fuzzy metric spaces, and some elementary fuzzy fractional calculus tools.…”
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Existence Analysis of Multi-Point Boundary Value Problems with Riesz-Caputo Fractional Derivatives by Takieddine Zeghida, Rabah Khaldi, Assia Guezane-Lakoud

“…We use Krasnoselskii's fixed point theorem and Leray-Schauder's nonlinear alternative to achieve this goal. …”
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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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Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions by Bashir Ahmad, Juan J. Nieto

“…The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space.…”
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On the Ulam stability and existence of $ L^p $-solutions for fractional differential and integro-differential equations with Caputo-Hadamard derivative by Abduljawad Anwar, Shayma Adil Murad

“…By employing Hölder's inequality together with the Krasnoselskii fixed-point theorem and the Banach contraction principle, the study establishes sufficient conditions for solving nonlinear problems. …”
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