Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 38Citation - Scopus: 39On the Mittag-Leffler Stability of Q-Fractional Nonlinear Dynamical Systems(Editura Acad Romane, 2011) Jarad, Fahd; Jarad, Fahd; Abdeljawad, Thabet; Abdeljawad, Thabet; Gundogdu, Emrah; Baleanu, Dumitru; Baleanu, Dumitru; MatematikIn this article, analogous to the definition of the exponential stability of ordinary dynamical systems and the Mittag-Leffler stability of the fractional dynamical systems, we consider the Mittag-Leffler stability for q-fractional nonlinear dynamical systems. The sufficient conditions for Mittag-Leffler stability of such dynamical systems within the framework of the q-fractional Caputo derivative are studied.Article Citation - WoS: 6Citation - Scopus: 5Fixed Points of Generalized Contraction Mappings in Cone Metric Spaces(Univ Osijek, dept Mathematics, 2011) Turkoglu, Duran; Abdeljawad, Thabet; Abuloha, Muhib; Abdeljawad, Thabet; MatematikIn this paper, we proved a fixed point theorem and a common fixed point theorem in cone metric spaces for generalized contraction mappings where some of the main results of Ciric in [8, 27] are recovered.Article Citation - WoS: 3Completion of Tvs-Cone Metric Spaces and Some Fixed Point Theorems(Gazi Univ, 2011) Abdeljawad, Thabet; Abdeljawad, Thabet; MatematikIn this paper a completion theorem for cone metric spaces and a completion theorem for cone normed space over a complete locally convex topological vector space E are proved. The completion spaces are defined by means of an equivalence relation obtained by convergence via the topology of the locally convex space E. Very recently some fixed point theorems obtained in cone Banach spaces are generalized to locally convex cone Banach spaces. These theorems can not be generalized or proved trivially by using the nonlinear scalarization function used very recently by Wei-Shih Du in " A note on cone metric fixed point theory and its equivalence, Nonlinear Analysis Theory Methods and Applications 72 (5):2259-2261 (2010)".Article Citation - WoS: 3Citation - Scopus: 3The Property of Smallness Up To a Complemented Banach Subspace(Kossuth Lajos Tudomanyegyetem, 2004) Abdeljawad, T; Abdeljawad, Thabet; Yurdakul, M; MatematikThis article investigates locally convex spaces which satisfy the property of smallness up to a complemented Banach subspace, the SCBS property, which was introduced by Djakov, Terzioglu, Yurdakul and Zahariuta. It is proved that a bounded perturbation of an automorphism on a complete barrelled locally convex, space with the SCBS is stable up to a Banach subspace. New examples are given, and the relation of the SCBS with the quasinormability is analyzed. It is proved that the Frechet space l(p+) does not satisfy the SCBS, therefore this property is not inherited by subspaces or separated quotients.Article Citation - WoS: 12Citation - Scopus: 15Variational Principles in the Frame of Certain Generalized Fractional Derivatives(Amer inst Mathematical Sciences-aims, 2020) Jarad, Fahd; Abdeljawad, ThabetIn this article, we study generalized fractional derivatives that contain kernels depending on a function on the space of absolute continuous functions. We generalize the Laplace transform in order to be applicable for the generalized fractional integrals and derivatives and apply this transform to solve some ordinary differential equations in the frame of the fractional derivatives under discussion.Review Variational principles in the frame of certain generalized fractional derivatives(Amer Inst Mathematical Sciences-AIMS, 2020) Jarad, Fahd; Abdeljawad, ThabetIn this article, we study generalized fractional derivatives that contain kernels depending on a function on the space of absolute continuous functions. We generalize the Laplace transform in order to be applicable for the generalized fractional integrals and derivatives and apply this transform to solve some ordinary differential equations in the frame of the fractional derivatives under discussion.Article Citation - WoS: 86Qualitative Analysis of a Mathematical Model in the Time of Covid-19(Hindawi Ltd, 2020) Mahariq, Ibrahim; Jarad, Fahd; Shah, Kamal; Abdeljawad, ThabetIn this article, a qualitative analysis of the mathematical model of novel corona virus named COVID-19 under nonsingular derivative of fractional order is considered. The concerned model is composed of two compartments, namely, healthy and infected. Under the new nonsingular derivative, we, first of all, establish some sufficient conditions for existence and uniqueness of solution to the model under consideration. Because of the dynamics of the phenomenon when described by a mathematical model, its existence must be guaranteed. Therefore, via using the classical fixed point theory, we establish the required results. Also, we present the results of stability of Ulam's type by using the tools of nonlinear analysis. For the semianalytical results, we extend the usual Laplace transform coupled with Adomian decomposition method to obtain the approximate solutions for the corresponding compartments of the considered model. Finally, in order to support our study, graphical interpretations are provided to illustrate the results by using some numerical values for the corresponding parameters of the model.Article Citation - Scopus: 4Nonlinear singular p-Laplacian boundary value problems in the frame of conformable derivative(American Institute of Mathematical Sciences, 2021) Bouloudene, Mokhtar; Alqudah, Manar A.; Jarad, Fahd; Adjabi, Yassine; Abdeljawad, ThabetThis paper studies a class of fourth point singular boundary value problem of p-Laplacian operator in the setting of a specific kind of conformable derivatives. By using the upper and lower solutions method and fixed point theorems on cones., necessary and sufficient conditions for the existence of positive solutions are obtained. In addition, we investigate the dependence of the solution on the order of the conformable differential equation and on the initial conditions. © 2021 American Institute of Mathematical Sciences. All rights reserved.Article Citation - WoS: 390Citation - Scopus: 406Generalized Fractional Derivatives and Laplace Transform(Amer inst Mathematical Sciences-aims, 2020) Jarad, Fahd; Abdeljawad, ThabetIn this article, we study generalized fractional derivatives that contain kernels depending on a function on the space of absolute continuous functions. We generalize the Laplace transform in order to be applicable for the generalized fractional integrals and derivatives and apply this transform to solve some ordinary differential equations in the frame of the fractional derivatives under discussion.Editorial Citation - WoS: 1Citation - Scopus: 1Recent Developments and Applications on Discrete Fractional Equations and Related Topics(Hindawi Ltd, 2013) Alzabut, Jehad; Sun, Shurong; Abdeljawad, Thabet