Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems by Mohamed Hannabou, Khalid Hilal, Ahmed Kajouni

“…By utilizing the theory of operators semigroup and fractional derivative, a new concept on a solution for our problem is introduced. We used some fixed point theorems such as Banach contraction mapping principle, Schauder’s fixed point theorem, Schaefer’s fixed point theorem, and Krasnoselskii’s fixed point theorem, and we derive many existence and uniqueness results concerning the solution for impulsive nonlocal Cauchy problems. …”
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Complete Controllability for Fractional Evolution Equations by Xia Yang, Haibo Gu

“…The paper is concerned with the complete controllability of fractional evolution equation with nonlocal condition by using a more general concept for mild solution. 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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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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Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral Conditions by Jessada Tariboon, Sotiris K. Ntouyas, Chatthai Thaiprayoon

“…We study existence and uniqueness of solutions for a problem consisting of nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions. A variety of fixed point theorems are used, such as Banach’s fixed point theorem, Krasnoselskii’s fixed point theorem, Leray-Schauder’s nonlinear alternative, and Leray-Schauder’s degree theory. …”
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Fractional Langevin Equations with Nonseparated Integral Boundary Conditions by Khalid Hilal, Lahcen Ibnelazyz, Karim Guida, Said Melliani

“…In this paper, we discuss the existence of solutions for nonlinear fractional Langevin equations with nonseparated type integral boundary conditions. The Banach fixed point theorem and Krasnoselskii fixed point theorem are applied to establish the results. …”
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A Study on ψ-Caputo-Type Hybrid Multifractional Differential Equations with Hybrid Boundary Conditions by Fouad Fredj, Hadda Hammouche, Mohammed S. Abdo, Wedad Albalawi, Abdulrazak H. Almaliki

“…Using an advantageous generalization of Krasnoselskii’s fixed point theorem, we establish results of at least one solution, whereas the uniqueness of solution is derived via Banach’s fixed point theorem. …”
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On a Nonlocal Multipoint and Integral Boundary Value Problem of Nonlinear Fractional Integrodifferential Equations by Lahcen Ibnelazyz, Karim Guida, Said Melliani, Khalid Hilal

“…First of all, we give some preliminaries and notations that are necessary for the understanding of the manuscript; second of all, we show the existence and uniqueness of the solution by means of the fixed point theory, namely, Banach’s contraction principle and Krasnoselskii’s fixed point theorem. …”
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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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Positive Solutions to a Second-Order Discrete Boundary Value Problem by Xiaojie Lin, Wenbin Liu

“…We are concerned with second-order discrete boundary value problems and obtain some sufficient conditions for the existence of at least one positive solution by using the fixed point theorem due to Krasnosel'skii on a cone.…”
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Existence of Almost Periodic Solutions for Impulsive Neutral Functional Differential Equations by Junwei Liu, Chuanyi Zhang

“…Our results are based on Krasnoselskii’s fixed-point theorem combined with an exponentially stable strongly continuous operator semigroup. …”
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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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Positive Solutions for a System of Fractional Differential Equations with Two Parameters by Hongyu Li, Junting Zhang

“…In this paper, the existence of positive solutions in terms of different values of two parameters for a system of conformable-type fractional differential equations with the p-Laplacian operator is obtained via Guo-Krasnosel’skii fixed point theorem.…”
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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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Positive Solution to a Fractional Boundary Value Problem by A. Guezane-Lakoud, R. Khaldi

“…By means of Banach contraction principle, Leray-Schauder nonlinear alternative, properties of the Green function, and Guo-Krasnosel'skii fixed point theorem on cone, some results on the existence, uniqueness, and positivity of solutions are obtained.…”
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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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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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New Existence Results for Nonlinear Fractional Integrodifferential Equations by Lahcen Ibnelazyz, Karim Guida, Khalid Hilal, Said Melliani

“…Some new existence and uniqueness results are proposed by using the fixed point theory. In particular, we make use of the Banach contraction mapping principle and Krasnoselskii’s fixed point theorem under some weak conditions. …”
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The Existence of Positive Solutions for Boundary Value Problem of the Fractional Sturm-Liouville Functional Differential Equation by Yanan Li, Shurong Sun, Zhenlai Han, Hongling Lu

“…By means of the Guo-Krasnoselskii fixed point theorem and the fixed point index theorem, some positive solutions are obtained, respectively. …”
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Positive Solutions of a Generalized Nonautonomous Fractional Differential System by Mohammed S. Abdo, Heba Y. Zahran, El Sayed Yousef, Emad E. Mahmoud, Abdel-Haleem Abdel-Aty

“…The analysis is based on Guo-Krasnoselskii’s and Banach’s fixed point theorem. Finally, we give two examples to verify our results.…”
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