Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Now showing 1 - 10 of 224
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    Performance Evaluation of Matched Asymptotic Expansions for Fractional Differential Equations With Multi-Order
    (Soc Matematice Romania, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Sayevand, Khosro; Matematik
    An extension of the concept of the asymptotic expansions method is presented in this paper. The multi-order differential equations of fractional order are investigated and the convergence of the proposed method is proven. The reported results show that the present approach is very effective and accurate and also are in good agreement with the ones in the literature.
  • Article
    Citation - WoS: 34
    Citation - Scopus: 30
    New Solutions of the Transport Equations in Porous Media Within Local Fractional Derivative
    (Editura Acad Romane, 2016) Zhang, Yu; Baleanu, Dumitru; Baleanu, Dumitru; Yang, Xiao-Jun; Matematik
    In this manuscript we use the series expansion method within local fractional derivative to obtain the solutions of both homogeneous and non-homogeneous transport equations. The new reported solutions are able to describe more efficiently the behavior of solutions of the transport phenomena in porous media.
  • Article
    Citation - WoS: 9
    Analytic Study of Allen-Cahn Equation of Fractional Order
    (int Center Scientific Research & Studies, 2017) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Baleanu, Dumitru; Matematik
    The key purpose of the present article is to analyze the Allen Cahn equation of fractional order. The fractional Allen-Cahn equation models the process of phase separation in iron alloys, along with order-disorder transitions. The analytical technique is employed to investigate the fractional model of Allen-Cahn equation. The numerical results are shown graphically. The outcomes show that the analytical technique is very efficient and user friendly for handling nonlinear fractional differential equations describing the real world problems.
  • Article
    Citation - WoS: 16
    Citation - Scopus: 17
    Fractional Synchronization of Chaotic Systems With Different Orders
    (Editura Acad Romane, 2012) Razminia, Abolhassan; Baleanu, Dumitru; Baleanu, Dumitru; Matematik
    In this paper, we consider two chaotic systems with different orders. First, we consider the case when one of them is fractional order (master system) and another one is integer order (slave system). Second, we consider the case when both of them are fractional order but the orders are different. Using a fractional synchronization scheme in the presence of discrepancy between initial conditions of these systems for both cases the trajectories of the slave system are forced to track the master system trajectories. The effectiveness of the proposed technique is verified by numerical simulations for Chen systems.
  • Article
    Citation - WoS: 21
    Citation - Scopus: 22
    A Discussion on the Role of People in Global Software Development
    (Univ Osijek, Tech Fac, 2013) Pusatlı, Özgür Tolga; Misra, Sanjay; Colomo-Palacios, Ricardo; Pusatli, Tolga; Soto-Acosta, Pedro; Yönetim Bilişim Sistemleri
    Literature is producing a considerable amount of papers which focus on the risks, challenges and solutions of global software development (GSD). However, the influence of human factors on the success of GSD projects requires further study. The aim of our paper is twofold. First, to identify the challenges related to the human factors in GSD and, second, to propose the solution(s), which could help in solving or reducing the overall impact of these challenges. The main conclusions of this research can be valuable to organizations that are willing to achieve the quality objectives regarding GSD projects.
  • Article
    Citation - WoS: 31
    Citation - Scopus: 34
    Transport Equations in Fractal Porous Media Within Fractional Complex Transform Method
    (Editura Acad Romane, 2013) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; He, Ji-Huan; Matematik
    In this paper we investigate the transport equations in fractal porous media by using the fractional complex transform method. The local fractional linear and nonlinear transport equations with local fractional time and space fractional derivatives are obtained. The proposed models adequately describe the fractal transport processes.
  • Article
    Citation - WoS: 59
    Citation - Scopus: 66
    New Aspects of the Motion of a Particle in a Circular Cavity
    (Editura Acad Romane, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Asad, Jihad H.; Jajarmi, Amin; Matematik
    In this work, we consider the free motion of a particle in a circular cavity. For this model, we obtain the classical and fractional Lagrangian as well as the fractional Hamilton's equations (FHEs) of motion. The fractional equations are formulated in the sense of Caputo and a new fractional derivative with Mittag-Leffler nonsingular kernel. Numerical simulations of the FHEs within these two fractional operators are presented and discussed for some fractional derivative orders. Numerical results are based on a discretization scheme using the Euler convolution quadrature rule for the discretization of the convolution integral. Simulation results show that the fractional calculus provides more flexible models demonstrating new aspects of the real-world phenomena.
  • Article
    Citation - WoS: 66
    Citation - Scopus: 63
    An Accurate Numerical Technique for Solving Fractional Optimal Control Problems
    (Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.; Abdelkawy, M. A.; Matematik
    In this article, we propose the shifted Legendre orthonormal polynomials for the numerical solution of the fractional optimal control problems that appear in several branches of physics and engineering. The Rayleigh-Ritz method for the necessary conditions of optimization and the operational matrix of fractional derivatives are used together with the help of the properties of the shifted Legendre orthonormal polynomials to reduce the fractional optimal control problem to solving a system of algebraic equations that greatly simplifies the problem. For confirming the efficiency and accuracy of the proposed technique, an illustrative numerical example is introduced with its approximate solution.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 2
    Solutions of Massless Conformal Scalar Field in an N-Dimensional Einstein Space
    (Jagiellonian Univ Press, 2008) Muslih, Sami I.; Baleanu, Dumitru; Baleanu, Dumitru; Rabei, Eqab M.; Matematik
    In this paper the wave equation for massless conformal scalar field in an Einstein's n-dimensional universe is solved and the eigen frequencies are obtained. The special case for alpha = 4 is recovered and the results are in exact agreement with those obtained in literature.
  • Article
    Citation - WoS: 38
    Citation - Scopus: 39
    On 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; Matematik
    In 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.