Browsing by Author "Defterli, Özlem"
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Conference Object About Some New Developments in Fractional Variational Principles(10th International Conference on Non-Integer Calculus and Its Applications (RRNR2018), 2018) Defterli, ÖzlemPublication Article Citation - WoS: 81Citation - Scopus: 94The Fractional Dynamics of a Linear Triatomic Molecule(Editura Acad Romane, 2021) Baleanu, Dumitru; Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Defterli, Özlem; Jajarmi, Amin; Defterli, Ozlem; Asad, Jihad H.; MatematikIn this research, we study the dynamical behaviors of a linear triatomic molecule. First, a classical Lagrangian approach is followed which produces the classical equations of motion. Next, the generalized form of the fractional Hamilton equations (FHEs) is formulated in the Caputo sense. A numerical scheme is introduced based on the Euler convolution quadrature rule in order to solve the derived FHEs accurately. For different fractional orders, the numerical simulations are analyzed and investigated. Simulation results indicate that the new aspects of real-world phenomena are better demonstrated by considering flexible models provided within the use of fractional calculus approaches.Article Citation - WoS: 104Citation - Scopus: 119Fractional Treatment: an Accelerated Mass-Spring System(Editura Acad Romane, 2022) Defterli, Ozlem; Baleanu, Dumitru; Baleanu, Dumitru; Defterli, Özlem; Jajarmi, Amin; Sajjadi, Samaneh Sadat; Alshaikh, Noorhan; Asad, Jihad H.; MatematikThe aim of this manuscript is to study the dynamics of the motion of an accelerated mass-spring system within fractional calculus. To investigate the described system, firstly, we construct the corresponding Lagrangian and derive the classical equations of motion using the Euler-Lagrange equations of integer-order. Furthermore, the generalized Lagrangian is introduced by using non-integer, so-called fractional, derivative operators; then the resulting fractional Euler-Lagrange equations are generated and solved numerically. The obtained results are presented illustratively by using numerical simulations.Book Part Hidden symmetries of two dimensional superintegrable systems(2007) Defterli, Özlem; Baleanu, DumitruClassification of the invariants of two - dimensional superintegrable systems is presented. The hidden symmetries associated to the existence of Killing - Yano tensors are investigated.Conference Object Infectious Disease Dynamics within Advanced Fractional Operators(2019) Defterli, Özlem; Arshad, Sadia; Jajarmi, AminArticle Citation - WoS: 5Citation - Scopus: 4Killing-Yano Tensors and Angular Momentum(inst Physics Acad Sci Czech Republic, 2004) Baleanu, D; Defterli, Z; Defterli, ÖzlemNew geometries were obtained by adding a suitable term involving the components of the angular momentum to the corresponding free Lagrangians. Killing vectors, Killing-Yano and Killing tensors of the obtained manifolds were investigated.Conference Object Killing-Yano Tensors, Surface Terms and Superintegrable Systems(Amer inst Physics, 2004) Baleanu, Dumitru; Baleanu, D; Defterli, Ö; Defterli, Özlem; MatematikKilling-Yano and Killing tensors are investigated corresponding to a set of two dimensional superintegrable systems. A suitable surface term is added to the corresponding free Lagrangian describing the motion of a particle on a 2-sphere of unit radius and we analyze the symmetries of the obtained geometries.Master Thesis Mathematical aspects of superintgrable systems(2004) Defterli, ÖzlemSuperintegrallenebilir SistemlerArticle Vester's sensitivity model for genetic networks with time-discrete dynamics(Springer International Publishing, 2014) Moreno, Liana Amaya; Defterli, Özlem; Fuegenschuh, Armin; Weber, Gerhard WilhelmWe propose a new method to explore the characteristics of genetic networks whose dynamics are described by a linear discrete dynamical model x(t+1) = Ax(t). The gene expression data x(t) is given for various time points and the matrix A of interactions among the genes is unknown. First we formulate and solve a parameter estimation problem by linear programming in order to obtain the entries of the matrix A. We then use ideas from Vester's Sensitivity Model, more precisely, the Impact Matrix, and the determination of the Systemic Roles, to understand the interactions among the genes and their role in the system. The method identifies prominent outliers, that is, the most active, reactive, buffering and critical genes in the network. Numerical examples for different datasets containing mRNA transcript levels during the cell cycle of budding yeast are presented
