Solvability of Some Fractional Boundary Value Problems with a Convection Term by Yongfang Wei, Zhanbing Bai

“…By the use of some fixed-point theorems and the properties of Green function, the existence results of at least one or triple positive solutions are presented. …”
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Existence Results for Fractional Semilinear Integrodifferential Equations of Mixed Type with Delay by Xue Wang, Bo Zhu

“…Based on the theories of resolvent operators, the measure of noncompactness, and the fixed point theorems, we establish the existence and uniqueness of global mild solutions for the equations. …”
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On Fractional Order Hybrid Differential Equations by Mohamed A. E. Herzallah, Dumitru Baleanu

“…We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order 0<α<1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. …”
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Fixed Point of Generalized Weak Contraction in b-Metric Spaces by Maryam Iqbal, Afshan Batool, Ozgur Ege, Manuel de la Sen

“…In this manuscript, a class of generalized ψ,α,β-weak contraction is introduced and some fixed point theorems in the framework of b-metric space are proved. …”
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Fixed Points for w-Contractive Multimaps by Abdul Latif, Marwan A. Kutbi

“…Using the generalized Caristi's fixed point theorems we prove the existence of fixed points for self and nonself multivalued weakly w-contractive maps. …”
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Some New Coupled Coincidence Point and Coupled Fixed Point Results in Partially Ordered Metric-Like Spaces and an Application by Min Liang, Chuanxi Zhu, Zhaoqi Wu, Chunfang Chen

“…Some new coupled coincidence point and coupled fixed point theorems are established in partially ordered metric-like spaces, which generalize many results in corresponding literatures. …”
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Common α-Fuzzy Fixed Point Results for Kannan Type Contractions with Application by Amer Hassan Albargi, Jamshaid Ahmad

“…The purpose of this paper is to utilize complex valued extended b-metric space and obtain common α-fuzzy fixed point theorems under Kannan type contractions. As application, we derive common α-fixed point results for multivalued mappings in the context of complex valued extended b-metric space.…”
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Existence and Uniqueness Results for Two-Term Nonlinear Fractional Differential Equations via a Fixed Point Technique by H. R. Marasi, H. Aydi

“…By virtue of recent fixed point theorems on mixed monotone operators, we get some new straightforward results with a wide range of applications.…”
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Some Theorems about (ψ,φ,ϵ,λ)-Contraction in Fuzzy Metric Spaces by Parvin Azhdari

“…We previously proved a number of fixed point theorems for some kinds of contractions like bn-contraction and φ-H contraction in fuzzy metric spaces. …”
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Existence Theorems for Fractional Semilinear Integrodifferential Equations with Noninstantaneous Impulses and Delay by Bo Zhu, Minhui Zhu

“…By the semigroup theory and fixed point theorems, we establish various theorems for the existence of mild solutions for the problem. …”
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Fixed points via a generalized local commutativity by Gerald F. Jungck

“…We thereby obtain new fixed point theorems for functions with bounded orbit(s) which generalize a recent theorem by Huang and Hong, and results by Jachymski, Jungck, Ohta, and Nikaido, Rhoades and Watson, and others.…”
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A Study of Caputo-Hadamard-Type Fractional Differential Equations with Nonlocal Boundary Conditions by Wafa Shammakh

“…Existence and uniqueness results of positive solutions to nonlinear boundary value problems for Caputo-Hadamard fractional differential equations by using some fixed point theorems are presented. The related Green’s function for the boundary value problem is given, and some useful properties of Green’s function are obtained. …”
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Fixed Point Problems in Cone Rectangular Metric Spaces with Applications by Muhammad Nazam, Anam Arif, Hasan Mahmood, Sang Og Kim

“…In this paper, we introduce an ordered implicit relation and investigate some new fixed point theorems in a cone rectangular metric space subject to this relation. …”
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On Generalized Rational α−Geraghty Contraction Mappings in G−Metric Spaces by N. Priyobarta, Bulbul Khomdram, Yumnam Rohen, Naeem Saleem

“…With this new contraction mapping, we establish some fixed-point theorems in G−metric space. The obtained result is verified with an example.…”
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Some Results on Generalized Pata–Suzuki Type Contractive Mappings by Merve Aktay, Murat Özdemir

“…In this work, we establish new fixed point theorems for generalized Pata–Suzuki type contraction via α-admissible mapping in metric spaces and to prove some fixed point results for such mappings. …”
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Common fixed points of single-valued and multivalued maps by Yicheng Liu, Jun Wu, Zhixiang Li

“…We define a new property which contains the property (EA) for a hybrid pair of single- and multivalued maps and give some new common fixed point theorems under hybrid contractive conditions. …”
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Existence Results for ψ-Hilfer Fractional Integro-Differential Hybrid Boundary Value Problems for Differential Equations and Inclusions by Chanakarn Kiataramkul, Sotiris K. Ntouyas, Jessada Tariboon

“…Existence results are established for single and multivalued cases, by using suitable fixed-point theorems for the product of two single or multivalued operators. …”
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Integral Type F-Contractions in Partial Metric Spaces by Vildan Ozturk

“…In this work, we defined generalized integral type F-contractions and proved common fixed point theorems for four mappings satisfying this type (Branciari type) of contractions in partial metric spaces.…”
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Existence of Nontrivial Solutions for Unilaterally Asymptotically Linear Three-Point Boundary Value Problems by Hongyu Li

“…Using fixed point theorems in ordered Banach spaces with the lattice structure, we consider the existence of nontrivial solutions under the condition that the nonlinear term can change sign and study the existence of sign-changing solutions for some second order three-point boundary value problems. …”
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Impulsive Fractional Semilinear Integrodifferential Equations with Nonlocal Conditions by Xue Wang, Bo Zhu

“…Based on the semigroup theory and some fixed point theorems, the existence theory of PC-mild solutions is established under the condition of compact resolvent operator. …”
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