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Article Citation - WoS: 146Citation - Scopus: 157On the Solutions of Fractional Differential Equations Via Geraghty Type Hybrid Contractions(Ministry Communications & High Technologies Republic Azerbaijan, 2021) Adiguzel, Rezan Sevinik; Sevinik Adıgüzel, Rezan; Aksoy, Umit; Aksoy, Ümit; Karapinar, Erdal; Karapınar, Erdal; Erhan, Inci M.; Erhan, İnci; Sevinik Adıgüzel, Rezan; Aksoy, Ümit; Karapınar, Erdal; Erhan, İnci; Mathematics; Mathematics; MathematicsThe aim of this article is twofold. Firstly, to study fixed points of mappings on b metric spaces satisfying a general contractive condition called Geraghty type hybrid contraction. Secondly, to apply the theoretical results to the problem of existence and uniqueness of solutions of boundary value problems with integral boundary conditions associated with a certain type of nonlinear fractional differential equations. The conditions for the existence of fixed points for Geraghty type hybrid contractions are determined and several consequences of the main results are deduced. Some examples on boundary value problems for nonlinear fractional differential equations of order 3 < alpha <= 4 are provided, where the existence and uniqueness of solutions are shown by using Geraghty type contractions.Article Citation - WoS: 2Uniqueness of Solution for Second Order Nonlinear q-difference Equations With Multi-Point and Integral Boundary Conditions(Yokohama Publ, 2022) Adiguzel, Rezan Sevinik; Sevinik Adıgüzel, Rezan; Sevinik Adıgüzel, Rezan; Mathematics; MathematicsThe existence and uniqueness of the solution for the boundary value problem associated with nonlinear second-order q-difference equation is discussed by Banach contraction mapping theorem on b-metric spaces. The problem is converted to an integral equation and investigated via a fixed point problem for an integral operator. Existence and uniqueness conditions for a fixed point of the integral operator are obtained. Moreover, an example is introduced to support the main results.Article Citation - WoS: 2Citation - Scopus: 1Spectrum of the q-schrodinger Equation by Means of the Variational Method Based on the Discrete q-hermite I Polynomials(World Scientific Publ Co Pte Ltd, 2021) Turan, Mehmet; Adiguzel, Rezan Sevinik; Calisir, Ayse DoganIn this work, the q-Schrodinger equations with symmetric polynomial potentials are considered. The spectrum of the model is obtained for several values of q, and the limiting case as q -> 1 is considered. The Rayleigh-Ritz variational method is adopted to the system. The discrete q-Hermite I polynomials are handled as basis in this method. Furthermore, the following potentials with numerous results are presented as applications: q-harmonic, purely q-quartic and q-quartic oscillators. It is also shown that the obtained results confirm the ones that exist in the literature for the continuous case.
