Search for dissertations about: "fractional differential equations"

Showing result 1 - 5 of 14 swedish dissertations containing the words fractional differential equations.

  2. 1. Modelling Stiffness and Damping by Use of Fractional Calculus with Application to Railpads

    Author : Åsa Fenander; Chalmers tekniska högskola; []
    Keywords : TEKNIK OCH TEKNOLOGIER; ENGINEERING AND TECHNOLOGY; stiffness; initial conditions; modal synthesis; time integration; measurements; fractional calculus; railway tracks; fractional integrals; damping; railpads; structural dynamics; fractional derivatives; mathematical models;

    Abstract : When studying the dynamic behaviour of a structure, e g a railway track, it is important for the analyst to model both stiffness and damping accurately. Mathematical models including fractional derivatives have been found to work well for many materials. Such models are linear and causal. READ MORE

  4. 2. Numerical Approximation of Solutions to Stochastic Partial Differential Equations and Their Moments

    Author : Kristin Kirchner; Göteborgs universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Petrov– Galerkin discretizations; Strong and weak convergence; Fractional operators; Finite element methods; Space-time variational problems; Tensor product spaces; Stochastic partial differential equations; White noise; Petrov– Galerkin discretizations;

    Abstract : The first part of this thesis focusses on the numerical approximation of the first two moments of solutions to parabolic stochastic partial differential equations (SPDEs) with additive or multiplicative noise. More precisely, in Paper I an earlier result (A. Lang, S. Larsson, and Ch. READ MORE

  5. 3. A Differentiable Approach to Stochastic Differential Equations : the Smoluchowski Limit Revisited

    Author : Haidar Al-Talibi; Astrid Hilbert; Yaozhong Hu; Linnéuniversitetet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; α-stable Lévy noise; Fractional Brownian motion; Girsanov theorem; Mean-field model; Nonlinear stochastic oscillator; Ornstein-Uhlenbeck process; Scaling limit; Second order Itô equation; Time change.; Matematik; Mathematics;

    Abstract : In this thesis we generalize results by Smoluchowski [43], Chandrasekhar[6], Kramers, and Nelson [30]. Their aim is to construct Brownian motion as a limit of stochastic processes with differentiable sample paths by exploiting a scaling limit which is a particular type of averaging studied by Papanicolao [35]. READ MORE

  6. 4. The Finite Element Method for Fractional Order Viscoelasticity and the Stochastic Wave Equation

    Author : Fardin Saedpanah; Göteborgs universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; finite element method; continuous Galerkin method; linear viscoelasticity; fractional calculus; fractional order viscoelasticity; weakly singular kernel; stability; a priori error estimate; a posteriori error estimate; stochastic wave equation; additive noise; Wiener process; strong convergence.; linear viscoelasticity;

    Abstract : This thesis can be considered as two parts. In the first part a hyperbolic type integro-differential equation with weakly singular kernel is considered, which is a model for dynamic fractional order viscoelasticity. In the second part, the finite element approximation of the linear stochastic wave equation is studied. READ MORE

  7. 5. Topics on fractional Brownian motion and regular variation for stochastic processes

    Author : Henrik Hult; KTH; []
    Keywords : stochastic processes; regular variation; extreme value theory; fractional Brownian motion; parameter estimation;

    Abstract : The first part of this thesis studies tail probabilities forelliptical distributions and probabilities of extreme eventsfor multivariate stochastic processes. It is assumed that thetails of the probability distributions satisfy a regularvariation condition. READ MORE