Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 6Citation - Scopus: 20Discussions on Proinov-Cb Mapping on B-Metric Space(Wiley, 2023) Fulga, Andreea; Karapinar, ErdalIn the present paper, we introduce the notion of Proinov-C-b-contraction mapping and we discuss it within the most interesting abstract structure, namely, b-metric spaces. We further take into consideration the necessary conditions to guarantee the existence and uniqueness of fixed points for such mappings, as well as indicate the validity of the main results by providing illustrative examples.Article Citation - WoS: 23Citation - Scopus: 26On the Boundary Value Problems of Hadamard Fractional Differential Equations of Variable Order(Wiley, 2023) Benkerrouche, Amar; Souid, Mohammed Said; Karapinar, Erdal; Hakem, AliIn this manuscript, we examine both the existence, uniqueness, and the stability of solutions to the boundary value problem (BVP) of Hadamard fractional differential equations of variable order by converting it into an equivalent standard Hadamard (BVP) of the fractional constant order with the help of the generalized intervals and the piecewise constant functions. All results in this study are established using Krasnoselskii fixed-point theorem and the Banach contraction principle. Further, the Ulam-Hyers stability of the given problem is examined, and finally, we construct an example to illustrate the validity of the observed results.Article Citation - WoS: 13Citation - Scopus: 15A Study on K-Generalized ?-Hilfer Fractional Differential Equations With Periodic Integral Conditions(Wiley, 2024) Bouriah, Soufyane; Benchohra, Mouffak; Lazreg, Jamal Eddine; Karapinar, Erdal; Salim, AbdelkrimThis paper deals with some existence and uniqueness results for a class of problems systems for nonlinear k-generalized psi-Hilfer fractional differential equations with periodic conditions. The arguments are based on Mawhins coincidence degree theory. Furthermore, an illustration is presented to demonstrate the plausibility of our results.Article Citation - WoS: 2Citation - Scopus: 3Soft Fixed Point Theorems for the Soft Comparable Contractions(Wiley, 2021) Xu, Zhi-Hao; Karapinar, Erdal; Chen, Chi-MingIn this article, we introduce the notions of a soft inf-comparable contraction and soft comparable Meir-Keeler contraction in a soft metric space. Furthermore, we prove two soft fixed point theorems which assure the existence of soft fixed points for these two types of comparable contractions. The obtained results not only generalize but also unify many recent fixed point results in the literature.Article Citation - WoS: 201Citation - Scopus: 178On the Solution of a Boundary Value Problem Associated With a Fractional Differential Equation(Wiley, 2024) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; Adiguzel, Rezan Sevinik; Sevinik Adigüzel, RezanThe problem of the existence and uniqueness of solutions of boundary value problems (BVPs) for a nonlinear fractional differential equation of order 2 < alpha <= 3 is studied. The BVP is transformed into an integral equation and discussed by means of a fixed point problem for an integral operator. Conditions for the existence and uniqueness of a fixed point for the integral operator are derived via b-comparison functions on complete b-metric spaces. In addition, estimates for the convergence of the Picard iteration sequence are given. An estimate for the Green's function related with the problem is provided and employed in the proof of the existence and uniqueness theorem for the solution of the given problem. Illustrative examples are presented to support the theoretical results.Article Citation - WoS: 17Citation - Scopus: 18On a Nonlocal Problem for a Caputo Time-Fractional Pseudoparabolic Equation(Wiley, 2021) Hammouch, Zakia; Karapinar, Erdal; Tuan, Nguyen Huy; Nguyen, Anh TuanIn this paper, we consider a class of pseudoparabolic equations with the nonlocal condition and the Caputo derivative. Two cases of problems (1-2) will be studied, which are linear case and nonlinear case. For the first case, we establish the existence, the uniqueness, and some regularity results by using some estimates technique and Sobolev embeddings. Second, the Banach fixed-point theorem will be applied to the nonlinear case to prove the existence and the uniqueness of the mild solution.