On a System of Volterra Type Hadamard Fractional Integral Equations in Fréchet Spaces by Saïd Abbas, Mouffak Benchohra, Yong Zhou

“…Our investigation is conducted with an application of an extension of the fixed point theorem of Burton-Kirk in Fréchet spaces.…”
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Existence Results for a Fully Fourth-Order Boundary Value Problem by Yongxiang Li, Qiuyan Liang

“…The discussion is based on the Fourier analysis method and Leray-Schauder fixed point theorem.…”
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Existence and Uniqueness of Positive Solutions to Nonlinear Second Order Impulsive Differential Equations with Concave or Convex Nonlinearities by Lingling Zhang, Chengbo Zhai

“…Using a new fixed point theorem of generalized concave operators, we present in this paper criteria which guarantee the existence and uniqueness of positive solutions to nonlinear two-point boundary value problems for second-order impulsive differential equations with concave or convex nonlinearities.…”
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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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SPDIEs and BSDEs Driven by Lévy Processes and Countable Brownian Motions by Pengju Duan

“…We prove the existence and uniqueness of the solutions to the backward stochastic differential equations by constructing Cauchy sequence and fixed point theorem. Moreover, we give a probabilistic solution of stochastic partial differential integral equations by means of the solution of backward stochastic differential equations. …”
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A Note on Fractional Equations of Volterra Type with Nonlocal Boundary Condition by Zhenhai Liu, Rui Wang

“…Firstly, by defining a weighted norm and using the Banach fixed point theorem, we show the existence and uniqueness of solutions. …”
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Complete Controllability of Fractional Neutral Differential Systems in Abstract Space by Fang Wang, Zhen-hai Liu, Jing Li

“…By using fractional power of operators and Sadovskii fixed point theorem, we study the complete controllability of fractional neutral differential systems in abstract space without involving the compactness of characteristic solution operators introduced by us.…”
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On the Well-Posedness of a Fractional Model of HIV Infection by Mohamed Jleli, Bessem Samet

“…Namely, using Grönwall’s lemma and Perov’s fixed point theorem, we obtain sufficient conditions for which the considered model admits a unique solution.…”
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Controllability of semilinear stochastic delay evolution equations in Hilbert spaces by P. Balasubramaniam, J. P. Dauer

“…The controllability of semilinear stochastic delay evolution equations is studied by using a stochastic version of the well-known Banach fixed point theorem and semigroup theory. An application to stochastic partial differential equations is given.…”
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Existence Results for Solutions of Integral Boundary Value Problems on Time Scales by Erbil Cetin, F. Serap Topal

“…We provide sufficient conditions for the existence of solutions by using Schauder fixed point theorem in a cone. Existence result for this problem is also given by the method of upper and lower solutions.…”
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Generalized Antiperiodic Boundary Value Problems for the Fractional Differential Equation with p-Laplacian Operator by Zhi-Wei Lv, Xu-Dong Zheng

“…Our results are based on fixed point theorem and contraction mapping principle. Furthermore, three examples are also given to illustrate the results.…”
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Multiple Positive Solutions for Singular Semipositone Periodic Boundary Value Problems with Derivative Dependence by Huiqin Lu

“…By constructing a special cone in C1[0,2π] and the fixed point theorem, this paper investigates second-order singular semipositone periodic boundary value problems with dependence on the first-order derivative and obtains the existence of multiple positive solutions. …”
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Existence and Uniqueness of Solutions for a Discrete Fractional Mixed Type Sum-Difference Equation Boundary Value Problem by Weidong Lv

“…By means of Schauder’s fixed point theorem and contraction mapping principle, we establish the existence and uniqueness of solutions to a boundary value problem for a discrete fractional mixed type sum-difference equation with the nonlinear term dependent on a fractional difference of lower order. …”
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Existence and Nonexistence of Positive Solutions for a Higher-Order Three-Point Boundary Value Problem by Yongping Sun, Qian Sun, Xiaoping Zhang

“…The existence results are obtained by applying a fixed point theorem of cone expansion and compression of functional type due to Avery, Henderson, and O’Regan.…”
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Successive Iteration and Positive Solutions for Nonlinear m-Point Boundary Value Problems on Time Scales by Yanbin Sang

“…Our approach is based on the monotone iterative technique and the cone expansion and compression fixed point theorem of norm type. Without the assumption of the existence of lower and upper solutions, we do not only obtain the existence of positive solutions of the problem, but also establish the iterative schemes for approximating the solutions.…”
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On Solutions to Fractional Iterative Differential Equations with Caputo Derivative by Alemnew Abera, Benyam Mebrate

“…First, the existence and uniqueness of the iterative fractional differential equation cDαcxt=ft,xt,xgxt are presented using the fixed-point theorem by imposing some conditions on f and g. …”
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A k-Dimensional System of Fractional Finite Difference Equations by Dumitru Baleanu, Shahram Rezapour, Saeid Salehi

“…We investigate the existence of solutions for a k-dimensional system of fractional finite difference equations by using the Kranoselskii’s fixed point theorem. We present an example in order to illustrate our results.…”
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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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An Extension of Generalized (𝜓,𝜑)-Weak Contractions by Tran Van An, Kieu Phuong Chi, Erdal Karapınar, Tran Duc Thanh

“…We prove a fixed-point theorem for a class of maps that satisfy generalized (𝜓,𝜑)-weak contractions depending on a given function. …”
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Existence and Uniqueness Theorem of Fractional Mixed Volterra-Fredholm Integrodifferential Equation with Integral Boundary Conditions by Shayma Adil Murad, Hussein Jebrail Zekri, Samir Hadid

“…Our analysis is based on an application of the Krasnosel'skii fixed-point theorem.…”
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