Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - Scopus: 1Qualitative Analysis of Nonlinear Hilfer Fractional Implicit Differential Equations in a Banach Space(DergiPark, 2023) Dhawan, K.; Vats, R.K.; Karapinar, E.This article focuses on the class of nonlinear implicit Hilfer-type fractional differential equations. By using the non-linear growth condition, we have derived the existence of at least one solution by applying Schauder’s fixed point theorem and using Lipschitz conditions, we have derived the uniqueness of the solution with the help of the Banach contraction principle. In addition, we have discussed the stability analysis by using Ulam-Hyers and Ulam-Hyers-Rassias stabilities. All results of this paper are established in a Banach space instead of R. We illustrate our results with the help of two examples. © 2023, DergiPark. All rights reserved.Article Citation - Scopus: 11An Open Discussion: Interpolative Metric Spaces(DergiPark, 2023) Karapınar, E.The main goal of this paper is to introduce a new abstract structure (so called, interpolative metric space) as a generalization of a standard metric space. We shall consider the analog of Banach Mapping Principle in the context of this new structure. © 2023, DergiPark. All rights reserved.Article Citation - Scopus: 4Numerical Construction of Lyapunov Functions Using Homotopy Continuation Method(DergiPark, 2022) Bala, S.I.; Ahmed, I.; Ibrahim, M.J.; Jarad, F.; Ibrahim, A.Lyapunov functions are commonly involved in the analysis of the stability of linear and nonlinear dynamical systems. Despite the fact that there is no generic procedure for creating these functions, many authors use polynomials in p-forms as candidates for constructing Lyapunov functions, while others restrict the construction to quadratic forms. We proposed a method for constructing polynomial Lyapunov functions that are not necessary in a form by focusing on the positive and negative definiteness of the Lyapunov candidate and the Hessian of its derivative, as well as employing the sum of square decomposition. The idea of Newton polytopes was used to transform the problem into a system of algebraic equations that were solved using the polynomial homotopy continuation method. Our method can produce several possibilities of Lyapunov functions for a given candidate. The sample test conducted demonstrates that the method developed is promising. © 2022, DergiPark. All rights reserved.Article Citation - Scopus: 45Interpolative Kannan-Meir Type Contraction(DergiPark, 2021) Karapınar, E.In this short manuscript, we revisit the renowned contraction’s of Meir-Keeler by involving the interpolation theory in the context of complete metric space. We provide a simple example to illustrate the validity of the observed result. © 2021, DergiPark. All rights reserved.Article Citation - Scopus: 2On Abstract Cauchy Problems in the Frame of a Generalized Caputo Type Derivative(DergiPark, 2023) Adjabi, Y.; Abdeljawad, T.; Mahariq, I.; Bourchi, S.; Jarad, F.In this paper, we consider a class of abstract Cauchy problems in the framework of a generalized Caputo type fractional. We discuss the existence and uniqueness of mild solutions to such a class of fractional differential equations by using properties found in the related fractional calculus, the theory of uniformly continuous semigroups of operators and the fixed point theorem. Moreover, we discuss the continuous dependence on parameters and Ulam stability of the mild solutions. At the end of this paper, we bring forth some examples to endorse the obtained results. © 2023, DergiPark. All rights reserved.