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Fractional Models and their Applications

  1. Research

    Boundedness and Lagrange stability of fractional order perturbed system related to unperturbed systems with initial time difference in Caputo's sense

    In this paper, we have investigated that initial time difference boundedness criteria and Lagrange stability for fractional order differential equation in Caputo's sense are unified with Lyapunov-like function...

    Coşkun Yakar, Muhammed Çiçek and Mustafa Bayram Gücen

    Advances in Difference Equations 2011 2011:54

    Published on: 10 November 2011

  2. Research

    Fractional order polytopic systems: robust stability and stabilisation

    This article addresses the problem of robust pseudo state feedback stabilisation of commensurate fractional order polytopic systems (FOS). In the proposed approach, Linear Matrix Inequalities (LMI) formalism i...

    Christophe Farges, Jocelyn Sabatier and Mathieu Moze

    Advances in Difference Equations 2011 2011:35

    Published on: 22 September 2011

  3. Research

    Point to point control of fractional differential linear control systems

    In the article, an alternative elementary method for steering a controllable fractional linear control system with open-loop control is presented. It takes a system from an initial point to a final point in a ...

    Andrzej Dzieliński and Wiktor Malesza

    Advances in Difference Equations 2011 2011:13

    Published on: 22 June 2011

  4. Research

    Bessel potential space on the Laguerre hypergroup

    In this article, we define the fractional differentiation D δ of order δ, δ > 0, induced by the Laguerre operator L and associated with respect to the Haar measure dm ...

    Taieb Ahmed

    Advances in Difference Equations 2011 2011:4

    Published on: 19 May 2011

  5. Research Article

    Existence Results for a Fractional Equation with State-Dependent Delay

    We provide sufficient conditions for the existence of mild solutions for a class of abstract fractional integrodifferential equations with state-dependent delay. A concrete application in the theory of heat co...

    José Paulo Carvalho dos Santos, Claudio Cuevas and Bruno de Andrade

    Advances in Difference Equations 2011 2011:642013

    Published on: 14 March 2011

  6. Research Article

    Numerical Solutions of a Fractional Predator-Prey System

    We implement relatively new analytical technique, the Homotopy perturbation method, for solving nonlinear fractional partial differential equations arising in predator-prey biological population dynamics syste...

    Yanqin Liu and Baogui Xin

    Advances in Difference Equations 2011 2011:190475

    Published on: 13 March 2011

  7. Research Article

    Time-Delay and Fractional Derivatives

    This paper proposes the calculation of fractional algorithms based on time-delay systems. The study starts by analyzing the memory properties of fractional operators and their relation with time delay. Based o...

    J.A. Tenreiro Machado

    Advances in Difference Equations 2011 2011:934094

    Published on: 13 March 2011

  8. Research Article

    From Newton's Equation to Fractional Diffusion and Wave Equations

    Fractional calculus represents a natural instrument to model nonlocal (or long-range dependence) phenomena either in space or time. The processes that involve different space and time scales appear in a wide r...

    Luis Vázquez

    Advances in Difference Equations 2011 2011:169421

    Published on: 10 March 2011

  9. Research Article

    Existence Results for Nonlinear Fractional Difference Equation

    This paper is concerned with the initial value problem to a nonlinear fractional difference equation with the Caputo like difference operator. By means of some fixed point theorems, global and local existence ...

    Fulai Chen, Xiannan Luo and Yong Zhou

    Advances in Difference Equations 2010 2011:713201

    Published on: 20 December 2010

  10. Research Article

    Fractional-Order Variational Calculus with Generalized Boundary Conditions

    This paper presents the necessary and sufficient optimality conditions for fractional variational problems involving the right and the left fractional integrals and fractional derivatives defined in the sense ...

    MohamedAE Herzallah and Dumitru Baleanu

    Advances in Difference Equations 2010 2011:357580

    Published on: 28 November 2010

  11. Research Article

    Fractional Odd-Dimensional Mechanics

    The classical Nambu mechanics is generalized to involve fractional derivatives using two different methods. The first method is based on the definition of fractional exterior derivative and the second one is b...

    Ali Khalili Golmankhaneh, AlirezaKhalili Golmankhaneh, Dumitru Baleanu and MihaelaCristina Baleanu

    Advances in Difference Equations 2010 2011:526472

    Published on: 27 October 2010