Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Book Part Citation - Scopus: 4Perov-Type Contractions(Springer, 2022) Karapınar, E.; Rakočević, V.; Yeşilkaya, S.S.; Cvetković, M.Article Citation - WoS: 91Citation - Scopus: 119A Discussion on the Existence of Positive Solutions of the Boundary Value Problems Via Ψ-Hilfer Fractional Derivative on B-Metric Spaces(Springer, 2020) Karapinar, Erdal; Afshari, HojjatIn this paper, we investigate the existence of positive solutions for the new class of boundary value problems via psi -Hilfer fractional differential equations. For our purpose, we use the alpha-psi Geraghty-type contraction in the framework of the b-metric space. We give an example illustrating the validity of the proved results.Article Citation - WoS: 7Citation - Scopus: 15Study on Pata E-Contractions(Springer, 2020) Fulga, Andreea; Aydi, Hassen; Karapinar, ErdalIn this paper, we introduce the notion of an alpha-(zeta) over tilde -E-Pata contraction that combines well-known concepts, such as the Pata contraction, the E-contraction and the simulation function. Existence and uniqueness of a fixed point of such mappings are investigated in the setting of a complete metric space. An example is stated to indicate the validity of the observed result. At the end, we give an application on the solution of nonlinear fractional differential equations.Article Citation - WoS: 20Citation - Scopus: 32Fixed Point Theory in the Setting of (α,β,ψ,φ)-Interpolative Contractions(Springer, 2021) Fulga, Andreea; Lopez de Hierro, Antonio Francisco Roldan; Erdal Karapinar; Roldán López de Hierro, Antonio Francisco; Karapınar, ErdalIn this manuscript we introduce the notion of (alpha,beta,psi,phi)-interpolative contraction that unifies and generalizes significant concepts: Proinov type contractions, interpolative contractions, and ample spectrum contraction. We investigate the necessary and sufficient conditions to guarantee existence and uniqueness of the fixed point of such mappings.Article Citation - WoS: 78Citation - Scopus: 95Existence and Ulam Stability for Impulsive Generalized Hilfer-Type Fractional Differential Equations(Springer, 2020) Benchohra, Mouffak; Karapinar, Erdal; Lazreg, Jamal Eddine; Salim, AbdelkrimIn this manuscript, we examine the existence and the Ulam stability of solutions for a class of boundary value problems for nonlinear implicit fractional differential equations with instantaneous impulses in Banach spaces. The results are based on fixed point theorems of Darbo and Monch associated with the technique of measure of noncompactness. We provide some examples to indicate the applicability of our results.Article Citation - WoS: 5Citation - Scopus: 6Application of Some Special Operators on the Analysis of a New Generalized Fractional Navier Problem in the Context of Q-Calculus(Springer, 2021) Ntouyas, Sotiris K.; Imran, Atika; Hussain, Azhar; Baleanu, Dumitru; Rezapour, Shahram; Etemad, SinaThe key objective of this study is determining several existence criteria for the sequential generalized fractional models of an elastic beam, fourth-order Navier equation in the context of quantum calculus (q-calculus). The required way to accomplish the desired goal is that we first explore an integral equation of fractional order w.r.t. q-RL-integrals. Then, for the existence of solutions, we utilize some fixed point and endpoint conditions with the aid of some new special operators belonging to operator subclasses, orbital alpha-admissible and alpha-psi-contractive operators and multivalued operators involving approximate endpoint criteria, which are constructed by using aforementioned integral equation. Furthermore, we design two examples to numerically analyze our results.Article Citation - WoS: 14Citation - Scopus: 10Advances on the Fixed Point Results Via Simulation Function Involving Rational Terms(Springer, 2021) Chen, Chi-Ming; Alghamdi, Maryam A.; Fulga, Andreea; Karapinar, ErdalIn this paper, we propose two new contractions via simulation function that involves rational expression in the setting of partial b-metric space. The obtained results not only extend, but also generalize and unify the existing results in two senses: in the sense of contraction terms and in the sense of the abstract setting. We present an example to indicate the validity of the main theorem.Article Citation - WoS: 15Citation - Scopus: 18A Study of Symmetric Contractions With an Application To Generalized Fractional Differential Equations(Springer, 2021) Karapinar, Erdal; Hussain, Aftab; Jarad, FahdThis article proposes four distinct kinds of symmetric contraction in the framework of complete F-metric spaces. We examine the condition to guarantee the existence and uniqueness of a fixed point for these contractions. As an application, we look for the solutions to fractional boundary value problems involving a generalized fractional derivative known as the fractional derivative with respect to another function.Article Analysis of the model of HIV-1 infection of CD4(+) T-cell with a new approach of fractional derivative(Springer, 2020) Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, ShahramBy using the fractional Caputo-Fabrizio derivative, we investigate a new version for the mathematical model of HIV. In this way, we review the existence and uniqueness of the solution for the model by using fixed point theory. We solve the equation by a combination of the Laplace transform and homotopy analysis method. Finally, we provide some numerical analytics and comparisons of the results.Article Citation - WoS: 160Citation - Scopus: 194A Fractional Differential Equation Model for the Covid-19 Transmission by Using the Caputo-Fabrizio Derivative(Springer, 2020) Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, DumitruWe present a fractional-order model for the COVID-19 transmission with Caputo-Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results with those of the Caputo derivative.